Two identical systems, with heat capacity at a constant volume that varies as C_v=bT^3 (where b is a constant) are thermally isolated. Initially, one…

Question

Two identical systems, with heat capacity at a constant volume that varies as C_v=bT^3 (where b is a constant) are thermally isolated. Initially, one system is at a temperature 100 K and the other is at 200K . The systems are then brought to thermal contact and the combined system is allowed to reach thermal equilibrium. If T0^4=n×10^8 K then what will be the value of n, where T_0 is the final temperature in kelvin?

MARKS Content Team · Accepted Answer

Correct answer: 8.5. Energy given by a system = Energy taken by another system dQ_1=dQ_2 ⇒ ∫100Tmc_vdT=-∫200Tmc_vdT ⇒ ∫100TbT^3dT=-∫200TbT^3dT⇒T^410T=-T^4200T ⇒ T^4-100^4=-T^4-200^4 ⇒ 2T^4=17×10^8⇒T=171 K ⇒ T^4=8.5×10^8 K

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