The temperature of an ideal gas in a sealed 0.5-m3 rigid container is reduced from 350 K to 270 K. The final pressure of the gas is 70 kPa. The molar heat capacity at constant volume of the gas is 28.0 J/mol · K. The heat absorbed by the gas is closest to

Answer :  The heat absorbed by the gas is closest to 34.9 kJ

Explanation :

First we have to calculate the moles of gas.

Using ideal gas equation:

where,

P = Pressure of gas = 70 kPa  = 70000 Pa

V = Volume of gas =

n = number of moles = ?

R = Gas constant =

T = Temperature of gas =

Putting values in above equation, we get:

Heat released at constant volume is known as internal energy.

The formula used for change in internal energy of the gas is:

where,

= heat at constant volume = ?  

= change in internal energy

n = number of moles of gas = 15.59 moles

= heat capacity at constant volume gas = 28.0 J/mol.K

= initial temperature = 350 K

= final temperature = 270 K

Now put all the given values in the above formula, we get:

Thus, the heat absorbed by the gas is closest to 34.9 kJ