JEE Advanced · 2024 · 26 May 2024 · Paper 1 · Heat & Thermodynamics

The specific heat capacity of a substance is temperature dependent and is given by the formula

C = k T

, where

k

is a constant of suitable dimensions in SI units, and

T

is the absolute temperature. If the heat required to raise the temperature of 1 kg of the substance from - 73°C to 27°C is n

k

, the value of n is ____.
[Given :

0 K = - 27 3^{\circ} C

Answer: 25000

Solution

Initial temperature:

T_{i} = - 7 3^{\circ} C = 200

K. Final temperature:

T_{f} = 2 7^{\circ} C = 300

K. Heat required:

Q = \int m C d T = \int_{200}^{300} 1 \cdot k T d T = k \int_{200}^{300} T d T = \frac{k}{2} [T^{2}]_{200}^{300} = \frac{k}{2} (30 0^{2} - 20 0^{2}) = \frac{k}{2} (90000 - 40000) = 25000 k

. Therefore,

n = 25000

JEE Advanced · 2024 · 26 May 2024 · Paper 1 · Integer answer

Practise more: all JEE Advanced PYQs on Heat & Thermodynamics →

More JEE Advanced questions on Heat & Thermodynamics

A quasi-static cycle of a monoatomic ideal gas contains an isothermal process $(a b)$ , followed by an isochoric process $(b c)$ and an adiabatic process $(c a)$ as shown in the figure. The volumes of th …
JEE Advanced 2026View solution →
As shown in the figure, five Carnot engines, each with efficiency $η$ and same number of cycles per unit time, are operating between six heat reservoirs. The amount of heat released per cycle by one engine is completely absorbed by the next engine. Consider $Q_{0}$ to …
JEE Advanced 2026View solution →
As shown in the figure, an insulated container is fitted with a thermally conducting but immovable partition $(P_{1})$ and a freely movable but thermally insulated piston $(P_{2})$ . The partition $P_{1}$ with thermal conductivity $K$ , cross sectional area A …
JEE Advanced 2026View solution →
Ten moles of an ideal monoatomic gas, initially in state $a$ at atmospheric pressure and temperature $T_{a} = 2 7^{\circ} C$ , is enclosed in a metal cylinder of volume $V_{0}$ fitted with a frictionless piston. The gas is suddenly compressed to state …
JEE Advanced 2026View solution →
Two identical plates P and Q, radiating as perfect black bodies, are kept in vacuum at constant absolute temperatures $T_{P}$ and $T_{Q}$ , respectively, with $T_{Q} < T_{P}$ , as shown in Fig. 1. The radia …
JEE Advanced 2025View solution →
The efficiency of a Carnot engine operating with a hot reservoir kept at a temperature of 1000 K is 0.4. It extracts 150 J of heat per cycle from the hot reservoir. The work extracted from this engine is being fully used to run a heat pump which has a coefficient of performance 1 …
JEE Advanced 2025View solution →