Two identical systems, with heat capacity at a constant volume that varies as C v = b T 3 (where b is a constant) are thermally isolated. Initially, one system is at a temperature 100   K and the other is at 200 K . The systems are then brought to thermal contact and the combined system is allowed to reach thermal equilibrium. If T 0 4 = n × 10 8   K then what will be the value of n , where T 0 is the

Step-by-step solution

Energy given by a system = Energy taken by another system d Q 1 = d Q 2 ⇒     ∫ 100 T m c v d T = - ∫ 200 T m c v d T ⇒   ∫ 100 T b T 3 d T = - ∫ 200 T b T 3 d T ⇒ T 4 10 T = - T 4 200 T ⇒       T 4 - 100 4 = - T 4 - 200 4 ⇒       2 T 4 = 17 × 10 8 ⇒ T = 171   K ⇒   T 4 = 8 . 5 × 10 8   K