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Standard XII

Physics

Heat Capacity

Block A of ma...

Question

Block A of mass 5 kg and temperature $300^{o} C$ . Block B of mass 10 kg and temperature $- 50^{o} C$ . The outer boundary of blocks are insulated such that heat lost to the surrounding is zero. Specific heat of block A and B be 1.0 and 0.4 kJ/kgK. The irreversibility of the system is (Take $T_{0}$ = 27°C)

276 kJ

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371 kJ

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527 kJ

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205 kJ

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Solution

The correct option is A 276 kJ

Given: $m_{A} = 5 k g, m_{B} = 10 k g, T_{A} = 573 K, T_{B} = 223 K, c_{A} = 1 k J / k g K, c_{B} = 0.4 k J / k g K$

Let final temperature be $T_{f}$ ,

By energy balance,

$\Rightarrow$ $m_{A} c_{A} [T_{A} - T_{f}] = m_{B} c_{B} [T_{f} - T_{B}]$

$\Rightarrow$ $5 \times 1 [573 - T_{f}] = 10 \times 0.4 [T_{f} - 223]$

$\Rightarrow$ $T_{f} = 417.4 K$

$S_{g e n} = m_{A} c_{A} l n \frac{T_{f}}{T_{A}} + m_{B} c_{B} l n \frac{T_{f}}{T_{B}}$

$= 5 \times 1 l n (\frac{417.4}{573}) + 10 \times 0.4 l n (\frac{417.4}{223})$

$= - 1.58 + 2.507 = 0.92 k J / K$

Irreversibility, $I = T_{0} Δ S = (273 + 27) \times 0.92$

$= 300 \times 0.92$

$= 276 k J$

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Block A of mass 5 kg and temperature 300oC. Block B of mass 10 kg and temperature −50oC. The outer boundary of blocks are insulated such that heat lost to the surrounding is zero. Specific heat of block A and B be 1.0 and 0.4 kJ/kgK. The irreversibility of the system is (Take T0 = 27°C)