A body of water loses energy at a constant rate. Assume tw+tixb/y iu-.1 rk uu1+m.cz ahat the specific heat caixr.mka+cb /+11iuuwutzy- . pacity of 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 soly3)pa : -xq4hwsven1nid 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 consta ;d1 0tz)hluusnt 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 temperauthu;sdl1 0) zture T of the water, with time t?

  Two solid substances of equal mass are heated with the z47)5 6 bhd2oos0 xvixx2tenisame power input. The graph below shows how the temperatures of the substance7 22d4nsi)vohxxt0oe5zib 6x s 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 miigs) sn/ohn n (rtgph:.c b4*3xture 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 beakerr (y,at)cb)xpe( tfv8o,m6 yr is positioned on an electronic balance. An immersion heater with a povot ramct8eryb,f, p6() x)y(wer rating of P is introduced into the water. 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. The graph shows the fhlf0x7bjb8p -7; bo lvariation of the temperature of the material bpflb 0job;8 -xh77flwith the energy supplied.

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

  A spherical object of surface area8+kx azqrlx-8 3 mi t2k( a(b;idkil9z $A$ 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 at a rate P. ptyj*f1*lrpifr 8+/m The graph shows the change in temperaturfji 8r1tmylfp *+p /r*e 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 capaciw v ibh)l19nutzv+tbn0(30 b/ujovj z.t1,rpty.
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*s.ldgalzrv /+j fc;* bgxg3: area 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 y3vu ,e b p+2iumi 0s3ho:qy8jtouching metal balls, each of mass 1.0 g and specific heat capaci+hujom,:2 bep3 u qsy3yv8 ii0ty 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 initial tv/3 * jp 6iy:lmdpnymx0i*ch*emperature 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 temperuti,dzhm 2: p,ature 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 change in average kino1s5lf)8xnd f;sew,:j/du ncetic energy of the molecules of a beaker of water as it is heated at a constant rate until it completely b d/;d8o5c l :f,sx1n un)fswjeoils 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 heated1 2lbday s q(g06e4w(fbrcv7 a with a heater of power P. Then the variation of temperature T of the liquidrv (7bd4bsea2fyw gc(01q6 la 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 hot plate. The chocolate is initiall q05ux 0gb*jdm+gy(cpy at its melting temperature of *5udxj0qgp0g cb( ym+$30^{\circ}C$.
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 rafr aalt4e5u1 afmo3,0ting of 2.8 kW heats liquid that flows through it. u3l e1,raf0 a a5tm4ofThe temperature of 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 surface area5-mp :0e rq auj0tnu0b $24.3\,cm^2$ 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 temperature5+leqif/ *blb -r8d:qv ,efl6/8fnt w,vo fkn T has surface area A and total radiation power P. If black body Y has temperature 2T and tob: ke/li8q*ref,n,qwbf n6vo d+f l-l5f t8v/ tal radiation power of 2P, what is the surface area of Y?

  A pendulum consists of a mass M w/ ar ntdw16v(cith a specific heat capacity 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 withcn v aw/tdr(61 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 melting temperature is placed in a massxg2tlb/ si)) lch 53bt M of water at an 3tcthb2l igxb5l) )/sinitial 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 hfl bf :or cuq(fd33-q8eat of fusion.
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 of a soli;t3c0a-wl*e rk hg, rqd wax block varies with time. The solid wax has a specificr ;-cgw*tae q,hr k30l 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 ypfw*7qmvbu7 ymu-9/ 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 latent heat of fusion L. The melting temperature of -qbymp/ uu7ywfmv97 * 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 nonqj upsks x0 u.;1wnm18-ideal gas with reference to the internal energy of the molecule k xu.wpn 81;ssumq0j1s.
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 h6w ,,hzfzkznfh r8p rl.gc +4f335eethe heating of 100 g of a substance is shown, from its state as a solidh g5 fzp.43r,ek +8fl,reh6n fz3whcz 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 (jl+9w;vuy zx;qkp/m9e g kl(a 4.0 kW electric heater causing it to melt. During 9(ykljmq/w ;kv9+; ezlp(gx uheating, 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 capac 9g1qfki(5fco,txbj s fj p0(0ity S is held in an insulated container of negligible mass. A x0( q1sj9tfc05ifob g f,p(jksecond 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 a j rafl;mt o44ur3*t,gnm 07mgt an absolute temperature T, in an enclosure of temperat f7agmmmnolgtur4* 0 j3r 4,;ture $T_s$​

  A hollow, insulated ring is packed with a w23z 4izc * fl3el)k hogcus6n4r t:(kmass M of ice pellets at an initial temperature of *sz(43)o ci6 r kgnl2zf3wuekc:4thl $0^{\circ}C$. 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 of ice, a mass m )r oo7ng (ika6of ice at a tempe7)( nk rai6oograture 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 $L_F$​?