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Question

The molar specific heat of oxygen at constant pressure $$C_{P} = 7.03\ cal/mol^{\circ}C$$ and $$R = 8.32\ J/mol^{\circ}C$$. The amount of heat taken by $$5$$ moles of oxygen when heated at constant volume from $$10^{\circ}C$$ to $$20^{\circ}C$$ will be approximately.


A
25 cal
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B
50 cal
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C
253 cal
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D
500 cal
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Solution

The correct option is C $$253\ cal$$
Given, $$C_{p} = 7.03\ cal/mol^{\circ}C,$$  $$ R = 8.315J/mol^{\circ}C = \dfrac{8.315}{4.2}  \ cal/mol^o C$$,
$$n = 5\ moles, T_{2} = 20^{\circ}C, T_{2} = 10^{\circ}C$$.
Heat taken at constant volume  $$ \triangle Q = nC_{V}\triangle T$$
$$\triangle Q= n(C_{P} - R)\triangle T$$          $$ [\because C_{P} - C_{V} = R]$$
$$\triangle Q= 5\left [7.03 - \dfrac {8.31}{4.2} \right ]\times (20 - 10)$$ $$= 253\ cal$$.

Physics

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