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
B
50 cal
C
253 cal
D
500 cal

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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