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

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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