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Two bodies of masses m1 and m2 and specific heat capacities s1 and s2 are connected by a rod of length l, cross-sectional area A, thermal conductivity K and negligible heat capacity. The whole system is thermally insulated. At time t = 0, the temperature of the first body is T1 and the temperature of the second body is T2(T2 > T1). Find the temperature difference between the two bodies at time t.

Two bodies of masses m1 and m2 and specific heat capacities s1 and s2 are connected by a rod of length l, cross-sectional area A, thermal conductivity K and negligible heat capacity. The whole system is thermally insulated. At time t = 0, the temperature of the first body is T1 and the temperature of the second body is T2(T2 > T1). Find the temperature difference between the two bodies at time t.

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
9 years ago
Sol. dθ/dt = 60/10 * 60 = 0.1°C/sec dQ/dt = KA/d (θ base 1 – θ base 2) = KA * 0.1/d + KA * 0.2/d + ………+ KA * 60/d = KA/d (0.1 + 0.2 + ………+ 60) = KA/d * 600/2 * (2 * 0.1 + 599 * 0.1) [∴ a + 2a + ………+ na = n/2{2a + (n - 1)a}] = 200 * 1 * 10^-4/20 * 10^-2 * 300 * (0.2 + 59.9) = 200 * 10^-2 * 300 * 60.1/20 = 3 * 10 * 60.1 = 1803 w = 1800 w

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