Question

At what temperature, the volume of V of a certain mass of gas at 37$^{o}C$ will be doubled, keeping the pressure constant?
(A) 327 $^{o}C$
(B) 347 $^{o}C$
(C) 527 $^{o}C$
(D) 54 $^{o}C$

Answer 1

Hint: The law of gas which contains terms like temperature, pressure, volume and gives a relation between them is known as ideal gas law. Ideal gas gives a relation between all the given terms i.e. PV=nRT.

Complete step by step solution:
Given in the question:
Pressure is constant
So the volume will be directly proportional to temperature
Given that the volume is doubled so the new volume will be 2V
And after doubling the volume let the new temperature to be ${{T}^{I}}$
Form the ideal gas equation:
PV=nRT
Or temperature T = $\dfrac{PV}{nR}$ (equation 1)
After doubling the volume:
\[P(2V)=nR{{T}^{I}}\]
So new temperature ${{T}^{I}}=\dfrac{2PV}{nR}$ (equation 2)
After comparing equation 1 and equation 2 we can say that
\[{{T}^{I}}=2T\]
Given temperature = 37$^{o}C$ = 310 K
Not new temperature =${{T}^{I}}=(2)(310)$ = 620 K = 347$^{o}C$

Hence the correct answer is option (B)

Additional information:
Ideal gas is derived from Boyle’s law, Charles law and Avogadro’s law. When these laws combine we get the ideal gas law.
Boyle's law = PV =K
Charles law= V =Kt
Avagadros law= V =Kn
We use the proportionality constant R which is the universal gas constant and we get the ideal gas equation as PV=nRT

Note: It is important to do the unit conversion from Celsius to Kelvin scale and from Kelvin to Celsius scale. To convert Kelvin scale to Celsius scale 273 is subtracted and to convert Celsius scale to Kelvin scale 273 is added. The value of the universal gas constant i.e. R depends on the unit of the measurement.