The temperature of an ideal gas in a sealed 0.1 m3 container is reduced from 430 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 work done by the gas is closest to:a) -42

b) -54

c) 54

d) 42

e) 0.00

Thus, the heat absorbed by the gas is closest to 13.97 kJ

Explanation:

First we have to calculate the moles of gas.

Using ideal gas equation:

PV=nRT

where,

P = Pressure of gas = 70 kPa  = 70000 Pa

V = Volume of gas = 0.1m^3

n = number of moles = ?

R = Gas constant =

T = Temperature of gas = 270K

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 = 3.118 moles

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

= initial temperature = 430 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 13.97 kJ