Answer to Question #71281 in Molecular Physics | Thermodynamics for Toms

Question

12 g of gas at a temperature of 7°C amounts to 0.004 m^3 volumes. After the gas is heated at constant pressure its density reaches 6*10 ^-4 g/cm^3.
to what temperature the gas is warmed up?

Answer 1

At first we need to convert given values to the same units:
V_1=0.004 m^3=4∙〖10〗^3 〖cm〗^3
To solve the problem the Ideal gas law need to be used:
pV=nRT
where p is pressure, V is volume of gas, n is number of moles, R – ideal gas constant and T is temperature.
Let’s define the ideal gas law for each system and write like the system of equations. The pressure and mole number still the same during the heating of the gas:

pV_1=nRT_1
pV_2=nRT_2

The dividing of 1st equation by 2nd equation gives simple ratio and after solution:
V_1/V_2 =T_1/T_2
T_2=T_1∙V_2/V_1
The value of V2 can be derived from the initial mass and final density:
V_2=m/d=12g/(6∙〖10〗^(-4) g/〖cm〗^3 )=2∙〖10〗^4 〖cm〗^3
The final temperature of the gas:
T_2=7℃ (2∙〖10〗^4 〖cm〗^3)/(4∙〖10〗^3 〖cm〗^3 )=35℃
Answer: the gas is warmed up to 35°C.