A body of water loses energy at a constant rate. Assume that the specific hearf5j c dy.h.6pt capacity of ice is half the specific heat capacity of liqui 6rdjp.5cyhf.d water.
Which graph shows a possible variation of temperature with time

  A chemical reaction occurs inside a solr8z/c;tkbx , 4b; zu1gbja-x pid of mass $m$ and specific heat capacity $c$. The initial temperature of the solid is $50\,K$.
What is the minimum energy that the reaction must release to increase the temperature of the solid to $100^{\circ}C$?

  An immersion heater of conj3v9er s(z 1e(glh, p60ju9ljxp b p;vstant power output is used to supply thermal energy to a cup of water at 373 K. The heater is turned on at time t=0. Which graph shows a possible variation of temperature T of the vzgp 1(jll;0 j3,rjpv6(euhbes 9xp9water, with time t?

  Two solid substances zp p; t)ik5t5oxla6)1mdw;-e:f4 +acb f bswqof equal mass are heated with the same power input. The graph below shows how the temperaturm+z )lbiww-tp) 5t:6eqs;5fd 1xc o;ba4ka f pes of the substances vary with time during heating.

Which of the following statements are correct?
I. Substance A has a lower specific heat capacity than Substance B when they are in the same physical state.
II. The specific heat capacity of each substance is lower in the solid state than the liquid state.
III. Substance A has a lower specific latent heat of fusion than Substance B.

  A sealed container contains a mixture / *5b yg 9nhs:6nxlo :czq8rmlof hydrogen and nitrogen gas.
The ratio ${mass\,of\,a\,hydrogen\,molecule}{mass\,of\,a\,nitrogen\,molecule}$=$\frac{1}{7}$The ratio $\frac{average\,kinetic\,energy\,of\,hydrogen}{average\,kinetic\,energy\,of\,nitrogen}$is

  In an experiment, a liquid-filled beaker is positioned on an electronic br1 aj)wl x-az+ u:hfs.alance. An immersion heater with a power rating of P is introduced into the water. Once the water begins to boil, a researcher monitored the change in mass m of the liquilar)j. h -azw:f+xs1u d over time t once the boiling commenced.

The theoretically predicted relationship between time $t$ and $m$ is $L_v$​=$frac{Pt}{C−m}$​
$C$ is the initial mass of the liquid when $t=0\,s$ and $L_v$​ is the latent heat of vaporisation of water.
1.Give the units of $L_v$​ in fundamental SI units.
2.In a particular experiment, the researcher uses a heater of power 65.0±0.1 W and measures m=0.120±0.001kg, C=0.125±0.001 kg, and t=600±1 s.
(1)Calculate the percentage error in the measured value of $L_v$​. $The\,percentage\,error\,of\,L_v$​
=    %
(2)For this experiment, calculate the value of $L_v$​ and its absolute uncertainty. $L_v$​ =    $\times10^6\,Jkg^{-1}$
(3)The accepted value of $L_v​$ is $2.3\times10^6\,Jkg^{−1}$. Explain why the experimental value does not match the accepted value.
3.The researcher plots a graph to show how m varies with $t$.
(1)Outline why P must be kept constant during the experiment.
(2)Assuming the relationship $L_v$​=$\frac{Pt}{C−m}$​ is correct, sketch the expected mass-time relationship on the axes below. (There is no need to put numbers to the axes).


(3)Outline how to obtain the value of $L_v$​ from the graph you have drawn in c(ii).

  Two ideal gases $A$ and $B$ of molar masses $m_A​>m_B$​ are initially at absolute temperatures $T_A​

  A material with a mass of m is heated. The graph shows the variation of the4d8 a4m go)zqx temperature of the material with the e)g4m4dq8 zxao nergy supplied.

Which one of the following gives the specific heat capacity of the material?

  A spherical object of surfs i0v v*8r+ e,0/k)yp wrxwktoace area $A$ and absolute temperature $T$ can be regarded as a black body. The power of the radiation emitted from the object is $P$. What would be the power of the radiation emitted by an object with an absolute temperature of $2T$and a surface area of $\frac{A}{2}$​?

  Water in a beaker is heated v f8c 0 xrg27g8nvc4w8 j4rkmaon a hot plate at a rate P. The graph shows the change in temperature of the water over tgr8 fvc 8x284 k4cvw0jm7ragnime.

Which graph correctly shows the new change in temperature of the water when the rate of thermal energy transfer is increased?
The original graph is shown by the dotted line.

  1,Define specific heat capps:x( z6eue r0 0xh4 q9o+upqsacity.
2,A sample of a substance initially in the solid state of mass of 200 g is heated by a heater of constant power. The variation of the temperature T with time t is shown on the graph below.

(1)The specific heat capacity of the sample in the liquid state is $1400\,J\,kg^{−1}K^{−1}$. Determine the power of the heater. P =    W
(2)Determine the specific latent heat of vaporization of the sample. L =   $J\,kg^{−1}$
(3)Explain, by considering the molecular model, why the time needed to boil the sample is more than the time needed for melting the same sample.
(4)It is realized that some of the sample in the liquid state evaporates during the heating process. State two differences between evaporation and boiling.

  An object has a surface 6ztw12 nvl jy7area of $2.0\,m^2$ and emissivity $e=0.5$. The object emits electromagnetic radiation of peak wavelength $2.90\times10^{−5}\,m$. What is the best estimate for the energy radiated by the object in one second?

  1.A “Newton's cradle” contains cqgtcsu/4e+iq60 7 jha row of five touching metal balls, each of mass 6tqj u0qh/ si cg47+ce1.0 g and specific heat capacity 400 $J\,kg^{-1}\,K^{−1}$, suspended from light strings of length 30 cm.
With its string kept taut, Ball 1 is released from rest at an angle of $60^{\circ}C$ to the vertical, causing it to collide with the other four balls. During every resulting collision, the moving ball comes to rest and most of its kinetic energy is transferred to the ball on the opposite end of the row. The remaining three balls remain stationary. It can be assumed that the size of each ball is negligible. $ΔT_{max}​$ =    mK

Assuming all energy from the ball is converted to thermal energy in the balls, determine the temperature increase of the five balls after the system has come to rest.
2.Explain why changing the mass of each ball, without altering its material, does not affect the final temperature.
3.(1)Balls 2-5 are replaced with an ice block of mass 9.0 g. Ball 1 is thrown horizontally so that it embeds itself in the ice at a velocity of 10.0 $m\,s^{−1}$. The ball/ice system slides frictionlessly along the surface after the collision. Determine speed of the system as it slides. $v_f$ =    $m\,s^{-1}$
(2)Show that the amount of energy converted to thermal energy in the collision is 45 mJ. $E_{heat}$ ​=    mJ
4.Estimate the percentage of the ice that melts, assuming that no energy is lost from the system. The system is at an initial temperature of $0^{\circ}C$.
Specific latent heat of fusion of ice = 333 $kJ\,kg^{−1}$ Percentage melted is therefore =    %

  Water of mass m at an 73 uw3e4dq p6nhjh9op (i(tix ov8lr8initial temperature of $20^{\circ}C$ oC is provided with thermal energy at a rate P. Its temperature rises to $30^{\circ}C$ in time t.
The rate of energy transfer is doubled and the mass of the water is halved. What is the final temperature, in time t, if the initial temperature is again $20^{\circ}C$?

  A hot sphere of tempera d1n0p qkbs/;mture T and surface area $A_1$​ radiates towards a metal plate of area $A_2$​ that is a very large distance D away. Which of the following expressions gives the rate at which radiant energy is received by the plate?

  Which of the graphs below best describes the ch h(jyd1:ey :* 0uq5zvgz x;yyaange in average kinetic energy of the 5d*(y qg0z1 yjuaev;:x:hzy ymolecules of a beaker of water as it is heated at a constant rate until it completely boils away?

  100 ml of water at $20^{\circ}C$ is poured in an aluminum container and heated at a constant rate until all of the water is boiled. After time $t_1$​ water starts to boil, and at time $t_2$ all of the water has boiled away.
Which of the following statements are correct?
I. If a glass container with the same mass is used instead of aluminum, $t_1$​ increases. ($c_glass$<$c_aluminum$​)
II. If the container with water is thermally isolated,$t_2$ decreases.
III. If more water is added to the container, $t_1$  increases.

  1.In an experiment, a beaker containing liquid of mass m is heated with a heaterqm967. xq8b gjus3vux of power P. Then the variation of temperature T of the lg7 ju3mbs qx8 v6x.uq9iquid with time t is recorded.

The data from the experiment is shown on the graph below.

(1)On the graph, draw the line of best fit for the data.
(2)Explain why it can not be concluded that the relationship between temperature and time is directly proportional.
2.Theory suggests that
$frac{T-T_0}{t}$=K
where$T_0$​ is the temperature when t=0 s.
(1)Using the data given, calculate the percentage uncertainty of $(T−T_0​$) at time 25s. $T_0$ =    %
(2)Use the graph to determine constant k.
(3)Theory also suggests that another expression for k is given by
$k=frac{P}{mc}$​, where c is another constant.
Determine the units of constant c, expressing your answer in fundamental SI units.

  A 100g chocolate bar isr yz bnvc1.m1bins2sdv1sid0g -9 ,x. placed onto a hot plate. The chocolate is initially at its melting temperatury.s1g.b dsb90is 2n-i,vzrx d11 cmnve of $30^{\circ}C$.
Heat is transferred from the plate to the chocolate at a constant rate $P_{in​}$ of 12W, causing it to melt at a constant rate of $6\,g\,min^{−1}$. After all the chocolate has melted, the liquid chocolate continues to heat to a temperature of $353\,K$.
Specific heat capacity of melted chocolate = $1.0\,kJkg^{−1}K^{−1}$
Specific latent heat of fusion of chocolate = $50\,Jg^{−1}$

1.State how the kinetic and potential energy of the chocolate change as it melts.
2.(1)Determine the amount of energy required to heat the liquid chocolate from the melting temperature to 353K. ΔE =    kJ
(2)Show that approximately 58% of the supplied energy is lost to the surroundings while the chocolate is melting. $As\,a\,percentage\,of\,the total energy, this\,gives$ =    %
3.The graph shows how the temperature of the chocolate changes with time.

Draw on the same graph a new line to show how temperature would change for a larger mass of chocolate with the same starting conditions.

  1.An electric heater with a power :v7 bgusw3*msqg.-/k j1pz h4g oewj 4rating of 2.8 kW heats liquid that flows through it. The temperature of the liquid increas *s v7w-3b: qp oh4gs jewj/gkugz14m.es from $18^{\circ}C$ to $38^{\circ}C$while passing through the heater. The flow rate of the liquid σ is $0.035\,kgs^{−1}$. Calculate the specific heat capacity of the liquid. c =    $J\,kg^{-1}\,K^{-1}$
2.Suggest whether your answer for (a) is above or below the actual value of the specific heat capacity. Justify your answer.

  1.An object X of surface are3f; vl::na- g2pawrtd j ni+2d g(l,xea $24.3\,cm^2$ emits 300W of radiation when its temperature is 1215K.
(1)State what is meant by emissivity.
(2)Show that this object is a blackbody radiator. e ≈   
2.Calculate the peak wavelength of the emitted radiation. $λ_{max}$ =    $\times10^{-6}\,m$
3.The object X is left to cool down until it reaches 800K. On the axes given, sketch the variation of intensity with wavelength of the radiation of object X at both the original 1215K and the cooler temperature of 800K. Label the graphs.

  Black body X at kelvin temperature T has surface area A and tota-j6zh(k6ywn0vpqgu- tj/y; yl radiation power P. If black kjvqtzwy(y-jhn 06y ;pu6g/-body Y has temperature 2T and total radiation power of 2P, what is the surface area of Y?

  A pendulum consists of a mass M with a specific heat capacity S suspen(+q0j k2 /qsstqmsq8pded from a point by a light string of length L. The pendulum is placed in an insulated container q/j 2+s8kpstsq 0(qmqfilled with a mass 2M of liquid with a specific heat capacity 2S. The pendulum is released from rest with the string horizontal. Assume that acceleration due to gravity is g and that both have the same starting temperature.

If all of the energy from the pendulum is converted to thermal energy, what is the temperature change of the liquid?

  An ice cube of mass m at its mek0/, a99j(mqpm *vugrdxi8 rolting temperature is placed in a mass M of water at an initial tem0amup(g8/9r,omxq 9ik vrd * jperature of $20^{\circ}C$. Assume that the specific heat capacity of liquid water is $4\,kJ\,kg\,K^{−1}$ and it has a specific latent heat of fusion of $320\,Jg^p{−1}$.

Assuming that the system is thermally isolated , what is the minimum value of M required for the ice to completely melt?

  1.Define the specific latent heat of fusion.hl76u0zn eljckh.82 m
2.An ice cube of temperature $-20^{\circ}C$ and mass 45g is placed in a bottle which is half filled with water of temperature $40^{\circ}C$and mass 1.2kg. Energy transfer only happens between the water and the ice.
The following data is available:
Specific latent heat of fusion of ice =$3.3\times10^5\,Jkg^{−1}$
Specific heat capacity of ice =$2.2\times10^3\,Jkg^{−1}K^{−1}$
Specific heat capacity of water = $4.2\times10^3$ $J$$kg^{−1}K^{−1}$
(1)Determine the final temperature T of the water. T =    $^{\circ}C$
(2)On the graph below, sketch how only the mass of water in the bottle varies with the temperature.
(no need to add values on the axes)

  The graph shows how the temperature fa mm*)dvpe99 kq(w9mof a solid wax block varies with time. The solid wax hm9) 9eawpf q9vmdk* m(as a specific heat capacity of $2\,kJ\,kg^{−1}K^{−1}$ and it absorbs heat at a rate of 20W.



What is the specific latent heat of fusion of wax?

  A thermally isolated system consists of a coin of weight mg and specific h2w oe-kdv kfvp i/lpy -g;uy m5e3)51yeat capacity c suspended in a vacuum at a vertical distance H above a solid block. The block has mass 4m, specific heat capacity 2c and latent heat of fusion L. The melting temperaturfp ylwm;5kk 5e2-oi) ydvu-ep3yg1 v/e of the block is an amount ΔT greater than the initial temperature of the block and the coin. The coin is dropped on to the block.


What is the minimum value of H required for the block to melt due to the collision?

  1.Distinguish between an ideal gas9wr 8xf ;6zamo and a non-ideal gas with reference to the internal energy of t ra 89o6zfx;wmhe molecules.
2.An ideal gas of mass 20g is heated in a sealed container. The temperature of the gas is increased from $127^{\circ}C$ to $327^{\circ}C$. The specific heat capacity of the gas at constant volume is $2.5\times10^4\,Jkg^{−1}K^{−1}$.
(1)Calculate the increase in total kinetic energy of the molecules of the ideal gas. The increase in total kinetic energy of the ideal gas is =    $\times10^5\,J$
(2)The average speeds of the molecules at $127^{\circ}C$ to $327^{\circ}C$ are $v_i$​ and $v_f$​ respectively. Calculate $\frac{v_i}{v_f}$​. $\frac{v_i}{v_f}$ =   

  A temperature-time graph for u(m-;dyg xvr.the heating of 100 g of a substance is shown, from its state a(- vgrd yu.;xms a solid to its state as a gas. The material is being heated in a well-insulated container at a constant heating rate of 50 W. It is assumed that mass remains constant and no heat is lost to the surroundings.

What is the specific heat capacity of the material in the liquid state?

  A substance, initially solid of mass 2.00 kg is heated by a 4.0 k: evm(t00c 0-q krixanW electric heater causing it to melt. During hxe(kvi r00-:mtcaqn0 eating, the substance also exchanges heat with its surroundings. The substance starts melting immediately and has fully turned to liquid after 400 s. Given that the specific latent heat of fusion of the solid is $900\,kJkg^{−1}$, what is the average rate of heat transfer between the substance and the surroundings in one second?

  A liquid of mass M, temperature 4T specific heat capacity S)6rjn jlo4hd485/titjhq i6t  is held in an insulated container of negligible mass. A sjtjri/tdth 5)qin6648l j4hoecond liquid of mass 2M, temperature T and specific heat capacity 3S is added to the container.
What is the equilibrium temperature of the mixture?

  A thin metal plate of mass m is held atlzo c )c.sk/rw xou1)9tfmu,; an absolute temperature T, in an enclosure of tem 19o;zrtxk fc/,co )umuls )w.perature $T_s$​

  A hollow, insulated ring is pac.bq38msy/f v1go glu/ked with a mass M of ice pellets at an initial temperatu/ 1 /ysb.vulg q38gmfore of $0^{\circ}C$. A mass 3M of steam is injected into the ring and circulates around it at an initial temperature of $100^{\circ}C$. Assume that the specific latent heat of vaporization is seven times the specific latent heat of fusion L.
L is also equal to the energy required to increase the temperature of a unit mass of liquid water by $80^{\circ}C$.


What are the final states of matter in the ring?

  In order to calculate the specific latent heat of fusion ofobw/ 2ol-im ov645o4 dmz h7xe:w /lsd ice, a mass m of ice at a t52l //s oi:-m 4ewhdo64zbvxdlo mo 7wemperature of $-2^{\circ}C$ was left inside a beaker until it changed into water at $20^{\circ}C$.


If q is the energy needed to make this change for 1 kilogram of ice, the specific heat capacity of ice is $c_i$​, the specific heat capacity of water is $c_w$​, and the specific latent heat of fusion of ice is $L_F$​.
Which expression gives the specific latent heat of fusion of ice $L_F$​?