Question

A gas expands from 1.5 L to 6.5 L against a constant pressure of 0.5 atm and during this process, the gas also absorbs 100J of heat . The change in internal energy is:
A. -153.3 J
B. 153.3 J
C. 306.6 kJ
D. 353.6 J

Answer 1

Hint: To find the change in internal energy we have to put the given values in the equation of internal energy the formula of internal energy that is $\Delta U=q+W$ where is the change in internal energy, q is the heat and W is the work done. Internal energy is related with the heat that is supplied to the system.

Complete step by step solution:
From your chemistry lessons you have learned about the law of thermodynamics. Here we are going to deal with the first law of thermodynamics.
First law of thermodynamics state that energy can neither be created nor be destroyed and according to it the change in the internal energy is equal to the sum of heat supplied to the system and the work done and it is expressed as,
\[\Delta U=q+W\]……………… (1)
Where,$\Delta U$= change in internal energy,
q = heat
and W = work done
As we know in gaseous phase work done is defined as the change in temperature and pressure. Hence it is written as,
\[W=-\Delta (PV)=-P\Delta V+(-V\Delta P)\]
Now, in the question it is given that pressure is constant, therefore $\Delta P$= 0,
Thus the equation of work done which we will use here is, $W=-P\Delta V$
Now, put this value of work done in equation (1), we will get
\[\Delta U=q-P\Delta V\]……………. (2)
 Here, $\Delta V$ is the change in volume and from the question, $\Delta V=6.5-1.5=5L$
In the question the value of pressure (P) = 0.5 atm and value of heat (q)= 100J
Here, we have to convert the Values into its S.I unit. After converting we will get:
$\Delta V=0.005\,{{m}^{-3}}$, q= 100 J and $P=0.5\times 101325\,pa$
Putting all the values in equation (2), we will get:
\[\Delta U=100-(0.5\times 101325\times 0.005)=-153.3J\]

Thus the correct option will be (A).

Note: Heat absorbed by the system can also regard the change in enthalpy and therefore change in enthalpy will be equal to heat. And if we have to calculate the change in enthalpy then we write the above formula of internal energy as $\Delta H=\Delta U-P\Delta V$ where $\Delta H$ is the change in enthalpy. Unit conversion is important and take care of the signs.