JEE Advanced 2025 · Paper 2

A temperature difference can generate e.m.f. in some materials. Let S be the e.m.f. produced per unit temperature difference between the ends of a wire, σ the electrical conductivity and κ the thermal conductivity of the material of the wire. Taking M, L, T, I and K as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity Z = S²σ/κ is:

1. A[M⁰L⁰T⁰I⁰K⁰]
2. B[M⁰L⁰T⁰I⁰K⁻¹]
3. C[M¹L²T⁻²I⁻¹K⁻¹]
4. D[M¹L²T⁻⁴I⁻¹K⁻¹]

Consider a star of mass m₂ kg revolving in a circular orbit around another star of mass m₁ kg with m₁ ≫ m₂. The heavier star slowly acquires mass from the lighter star at a constant rate of γ kg/s. In this transfer process, there is no other loss of mass. If the separation between the centers of the stars is r, then its relative rate of change 1/r dr/dt (in s⁻¹) is given by:

1. A−3γ/(2m₂)
2. B−2γ/m₂
3. C−2γ/m₁
4. D−3γ/(2m₁)

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 10. The hot reservoir of the heat pump is at a temperature of 300 K. Which of the following statements is/are correct:

1. AWork extracted from the Carnot engine in one cycle is 60 J.
2. BTemperature of the cold reservoir of the Carnot engine is 600 K.
3. CTemperature of the cold reservoir of the heat pump is 270 K.
4. DHeat supplied to the hot reservoir of the heat pump in one cycle is 540 J.