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Heat of Reaction

A vessel of v...

Question

A vessel of volume $0.2 m^{3}$ contains hydrogen gas at temperature $300 K$ and pressure $1 b a r$ . Find the heat (in kcal) required to raise the temperature to $400 K$ . (The molar heat capacity of hydrogen at constant volume is $5 c a l / m o l K$ )

4

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Solution

The correct option is A $4$
Using the equation $P V = n R T$ we have
$0.2 \times 10^{5} = n \times 8.314 \times 300$
Thus we get n as 8 moles.
Now the heat absorbed is given as
$Q = W + U = n R Δ T + n C_{v} Δ T$
or
$Q = n (1 + \frac{3}{2}) R Δ T$
or
$Q = 8 \times \frac{5}{2} \times 1.987 \times 100 = 4000 k c a l$

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