Answer to Question #8147 in Molecular Physics | Thermodynamics for Frank Omorogbe
Question #8147
A gas occupies a certain volume at 27 degree Celsius. If it is heated at constant pressure, its volume is exactly doubled at a temperature of _____________
A: 54 degrees celcius
B: 219 degrees celcius
C: 327 degrees celcius
D: 600 degree celcius
A: 54 degrees celcius
B: 219 degrees celcius
C: 327 degrees celcius
D: 600 degree celcius
Expert's answer
Let's use the ideal gas law:
P*V = v*R*T.
Let assume T0 = 27° C. As pressure P is constant, then
2*P*V = v*R*T1 ==> T1 = 2*P*V/(v*R) = 2*(P*V)/(v*R) = 2*(v*R*T0)/(v*R) = 2*T0.
So, the volume doubles when the temperature doubles. Here doubled temperature is
T1 = 2*27 = 54° C.
P*V = v*R*T.
Let assume T0 = 27° C. As pressure P is constant, then
2*P*V = v*R*T1 ==> T1 = 2*P*V/(v*R) = 2*(P*V)/(v*R) = 2*(v*R*T0)/(v*R) = 2*T0.
So, the volume doubles when the temperature doubles. Here doubled temperature is
T1 = 2*27 = 54° C.
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