A body of water loses energy at a constant rate. Assume that the specific heat ss/, n6pk (o/(;sm0lxb mvnza capacity /o 0s s,bxzslk m/m(6nnv(a;pof ice is half the specific heat capacity of liquid water.
Which graph shows a possible variation of temperature with time

  A chemical reaction occurs inside a solid of kej li.66rjf3/ zink*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 constant power output is used to suppl2pyfc,0ws h6ry 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 t r,2hw0cpfs 6yemperature T of the water, with time t?

  Two solid substances of equal mass are heated with the same power vuc4da.z2lor1 *ec: u input. The graph below shows how the temperatures of the substances vard1.c cvu2e*a: luz4 ory 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 c esh4 j ;v(0usjt9epacrg34r* ontains a mixture of 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 electro/ik n:8hhm.h)wg(s s jnic balance. An immersion heater with a power rating of P is introduced into the wat.s8g)/(: jmhkh shiwner. Once the water begins to boil, a researcher monitored the change in mass m of the liquid 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. Therf*pqj0s7*z mn3kh:r graph shows the variation of the temperature of the material kn:r*rqm*j p fzh7 0s3with the energy supplied.

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

  A spherical object of surfyac03:u9s-c i-ctaf face 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 on a hot plate a+ upzuop89zn : twu r4/2c)zqvt a rate P. The graph shows the change in tempezz+npuvzw/cu9 :2op4tqur) 8rature of the water over time.

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 capagl+ht6 d;gr x/iu yw-0city.
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 ar2 u*nvenig/,l/y as /m c8zg.oea 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 a row of five touching metal balls, each of m-m fd dvmld8/9ass 1.0 g and specid9m8d ml-dv/ ffic 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 ir0k-een:q.r4q : +(4wrq klbh nhrn(b nitial 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 temperature T and surf(1tqr hrv3r7 race 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 desc7rp)ux* 4 1h rt*uc/lifi+ivcribes the change in average kinetic energy of the molecules oi+i1l)u 4rc pv*/h7ictur xf*f 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 m76 4c hcv o9piwhdo02xass m is heated with a heater of power P. Then the variation of 0c7cp vi4wh hx29od6otemperature T of the liquid 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 is placed onto a ho,2vbl kn1:bd 9l/pgiqt plate. The chocolate is initially at its melting temperatu9bn: 1d /p2l,bkliqg vre 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 pows jlt)5y u1d0c2x ung fgg*.7mer rating of 2.8 kW heats liquid that flows through it. The temperature o1umd5yx st)c ufl07gnjg 2g*.f the liquid increases 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 sur,h) 3 ,lbcxh434zufyyrnc ) gj9iqpb+face area $24.3\,cm^2$ 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 total radiation pofuoy(bq-jyn9+ t0 lx 1wer P. If black body Y has temperature 2T and total radiation power of 2P, whatnjty +-0qbxfl(9 o1uy is the surface area of Y?

  A pendulum consists of a mass M with a specific heat capacityylzoysh f (cm.7xh6.5 S suspended from a point by a light string of length L. The pendulum is placed in an insulated container filled 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 hmly.oc 75s.(z6f yhx 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 melting temperature is pl8u x ro 5c,/hu9pmcb3(*ejn nnaced in a mass M of water at a,c (xuoje8/m 3hpbn5n9uc rn*n initial temperature 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 fusle5 tkwr:faz,xq p71; ion.
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 tempera,rr67urk r rs (bi)qjib7: p2zture of a solid wax block varies with time. The solid wax has abrp u:,7rqjbisri6 r )r(72z k 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 syq h-ir 6naxe.t 60 pk.l/fq)ssstem consists of a coin of weight mg and specific heat 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 laten ans6x).pfhtiqsrl0ek/ . 6-q t heat of fusion L. The melting temperature 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 gas and a non-ideal gas with reference to l32le qd3bxvn0d .a7lthe intexl0q ba73 2vne.l3dl drnal energy of the 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 nc1zmt 8)yy (kthe heating of 100 g of a substance is shown, from its state as 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 rtzny 81yc)km (emains 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 kW elecy/.9wlnbe ap;:g pic+tric heater causing it to melt. During heating, the substance also exchanges heat with its surroundings. The substance starts melting immediately and has fully turned to liquid after 400 s. Given th+pby;: wl/aigpn e9. cat 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 /ty72/* f-rmup 6bhqi- rqfvgspecific heat capacity S is held in an insulated container of negligiblehv-fp/r uqyg-f72 6/irm * qtb mass. A second 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, e4 o-pnjrp8t at an absolute temperature T, in an enclosuj8 e,4rtn-po pre of temperature $T_s$​

  A hollow, insulated ring is packed witz. p sgwt5,(ww0u 2mpkh a mass M of ice pellets at an initial temzww.gump2( ,s0pt k5wperature 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 l/o je a7*u; -f e7n8u5bilryxthe specific latent heat of fusion of ice, a mass m of ice at a b7n7auiro*;je uy-/ef8xl l 5temperature 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 $L_F$​?