Thermometry and Calorimetry | JEE Main previous year questions with Solutions

Q 1 :

On Celsius scale the temperature of body increases by 40°C. The increase in temperature on Fahrenheit scale is [2024]

68° F
70° F
72° F
75° F

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(3)

$\frac{C - 0}{100} = \frac{F - 32}{180}$

$C = \frac{5}{9} (F - 32) \Rightarrow ∆ C = \frac{5}{9} ∆ F$

$40 = \frac{5}{9} ∆ F \Rightarrow ∆ F = 72^{o} F$

$∴$ $40^{o}$ change on Celsius scale will corresponds to $72^{o}$ change on Fahrenheit scale.

Q 2 :

A block of ice at −10°C is slowly heated and converted to steam at 100°C. Which of the following curves represent the phenomenon qualitatively? [2024]

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(4)

$- 10 ° C ice \to_{change}^{Temp .} 0 ° C ice \to_{change}^{Temp .} 0 ° C$

$water \to_{change}^{Temp .} 100 ° C water \overset{Phase change}{\to} 100 ° C steam$

In this process, there are two phase changes and two temperature changes.

Q 3 :

An amount of ice of mass $10^{- 3}$ kg and temperature –10°C is transformed to vapour of temperature 110°C by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice = $2100 J {kg}^{- 1} K^{- 1}$ , specific heat of water = $4180 J {kg}^{- 1} K^{- 1}$ , specific heat of steam = $1920 J {kg}^{- 1} K^{- 1}$ , Latent heat of ice = $3.35 \times 10^{5} J {kg}^{- 1}$ and Latent heat of steam = $2.25 \times 10^{6} J {kg}^{- 1}$ ) [2025]

3022 J
3043 J
3003 J
3024 J

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(2)

First, Ice at –10°C $\overset{△ Q_{1}}{\to}$ Ice at 0°C $\overset{△ Q_{2}}{\to}$ Water at 0°C. Then, Water at 0°C $\overset{△ Q_{3}}{\to}$ Water at 100°C $\overset{△ Q_{4}}{\to}$ Vapour at 100°C $\overset{△ Q_{5}}{\to}$ Vapour at 110°C

$△ Q_{1} = m \times S_{I} \times △ T = 10^{- 3} \times 2100 \times 10 = 21 J$

$△ Q_{2} = m \times L_{f} = 10^{- 3} \times 3.35 \times 10^{5} = 335 J$

$△ Q_{3} = m \times S_{w} \times △ T = 10^{- 3} \times 4180 \times 100 = 418 J$

$△ Q_{4} = m \times L_{v} = 10^{- 3} \times 2.25 \times 10^{6} = 2250 J$

$△ Q_{5} = m \times S_{v} \times △ T = 10^{- 3} \times 1920 \times 10 = 19.2 J$

$△ Q_{net} = 3043.2 J$

Q 4 :

A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J, then the mass of the bullet is ______ grams.

(Latent heat of fusion of lead $= 25 \times 10^{4} J {Kg}^{- 1}$ and specific heat capacity of lead $= 125 J {Kg}^{- 1} K^{- 1}$ ) [2025]

20
15
10
5

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(3)

$Q = m s △ T + m L$

$625 = m \times 125 \times 300 + m \times 2.5 \times 10^{4}$

$625 = m {3.75 + 2.5} \times 10^{4}$

$\Rightarrow m = \frac{625}{625} \times 10^{- 4} kg = 10 g$

Q 5 :

Which of the following figure represents the relation between Celsius and Fahrenheit temperatures? [2025]

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(2)

$\frac{C}{5} = \frac{F - 32}{9} \Rightarrow C = \frac{5 F}{9} - \frac{160}{9}$

Clearly slope is +ve and intercept is –ve

Q 6 :

Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool. (Take, g = 10 $m / s^{2}$ specific heat of water = 4200 J/(kg K)) [2025]

0.23 K
0.36 K
0.14 K
0.48 K

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(4)

$m g h = m s △ T$

$\Rightarrow △ T = \frac{g h}{s} = \frac{10 \times 200}{4200} = 0.48 K$

Q 7 :

1 g of a liquid is converted to vapour at $3 \times 10^{5} Pa$ pressure. If 10% of the heat supplied is used for increasing the volume by $1600 {cm}^{3}$ during this phase change, then the increase in internal energy in the process will be: [2023]

$4800 J$
$4320 J$
$4.32 \times 10^{8} J$
$432000 J$

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(2)

$Work done = P Δ V$

$= 3 \times 10^{5} \times 1600 \times 10^{- 6} = 480 J$

Only 10% of heat is used in work done.

$Hence Δ Q = 4800 J$

The rest goes into internal energy, which is 90% of heat.

$Change in internal energy = 0.9 \times 4800 = 4320 J$

Q 8 :

Heat energy of 184 kJ is given to ice of mass 600 g at $- 12 ° C$ . Specific heat of ice is 2222.3 $J$ ${kg}^{- 1^{o}}$ $C^{- 1}$ and latent heat of ice is $336$ $kJ / {kg}^{- 1}$ . [2023]

(A) Final temperature of the system will be $0 ° C$ .

(B) Final temperature of the system will be greater than $0 ° C$ .

(C) The final system will have a mixture of ice and water in the ratio of 5 : 1.

(D) The final system will have a mixture of ice and water in the ratio of 1 : 5.

(E) The final system will have water only.

Choose the correct answer from the options given below:

A and D only
B and D only
A and E only
A and C only

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(1)

$Δ Q = 184 \times 10^{3}$

$m = 0.600 kg at - 12 ° C$

$S = 2222.3 J/kg/ ° C$

$L = 336 \times 10^{3} J/kg$

$Q_{1} = 0.600 \times 2222.3 \times 12 = 16000.56 J$

Remaining heat:

$Δ Q_{1} = 184000 - 16000.56 = 167999.44 J$

For melting at $0 ° C$

$Δ Q_{2} = 0.600 \times 336000 = 201600 J (needed)$

$∴$ $100% ice is not melted$

Amount of ice melted

$167999.44 = m \times 336000$ $= 0.4999 kg$

$∴$ $Mass of water = 0.4999 kg$

$Mass of ice = 0.1001 kg$

$∴$ $Ratio = \frac{0.1001}{0.4999} \approx 1 : 5$

Q 9 :

The graph between two temperature scales P and Q is shown in the figure. Between the upper fixed point and the lower fixed point, there are 150 equal divisions of scale P and 100 divisions on scale Q. The relationship for conversion between the two scales is given by [2023]

[IMAGE 88]

$\frac{t_{P}}{100} = \frac{t_{Q} - 180}{150}$
$\frac{t_{Q}}{150} = \frac{t_{P} - 180}{100}$
$\frac{t_{P}}{180} = \frac{t_{Q} - 40}{100}$
$\frac{t_{Q}}{100} = \frac{t_{P} - 30}{150}$

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(4)

$\frac{reading on scale - lower fixed point}{upper fixed point - lower fixed point} = constant$

$\frac{t_{p} - 30}{180 - 30} = \frac{t_{0} - 0}{100 - 0}$

$\frac{t_{p} - 30}{150} = \frac{t_{0}}{100}$

Q 10 :

For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure.

[IMAGE 89]

The temperature corresponding to the point ‘K’ is: [2023]

−273°C
−100°C
−373°C
−40°C

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(1)

$For isochoric process,$

$\frac{P}{T} = n \frac{R}{V} = constant$

$P = \frac{n R}{V} (t + 273)$

$If P = 0 \Rightarrow t = - 273 ° C$

Topic Question Set

Q 1 :

On Celsius scale the temperature of body increases by 40°C. The increase in temperature on Fahrenheit scale is [2024]

Q 2 :

A block of ice at −10°C is slowly heated and converted to steam at 100°C. Which of the following curves represent the phenomenon qualitatively? [2024]

Q 5 :

Which of the following figure represents the relation between Celsius and Fahrenheit temperatures? [2025]

Q 6 :

Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool. (Take, g = 10 $m / s^{2}$ specific heat of water = 4200 J/(kg K)) [2025]

Q 7 :

1 g of a liquid is converted to vapour at $3 \times 10^{5} Pa$ pressure. If 10% of the heat supplied is used for increasing the volume by $1600 {cm}^{3}$ during this phase change, then the increase in internal energy in the process will be: [2023]

Q 9 :

The graph between two temperature scales P and Q is shown in the figure. Between the upper fixed point and the lower fixed point, there are 150 equal divisions of scale P and 100 divisions on scale Q. The relationship for conversion between the two scales is given by [2023]

[IMAGE 88]

Q 10 :

For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure.

[IMAGE 89]

The temperature corresponding to the point ‘K’ is: [2023]

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