Question

A gaseous system releases 14 J of heat and increases its internal energy by 16 J. Which of the following statements is correct?

The volume of the system decreases and a positive amount of work is done.

The volume of the system increases and a negative amount of work is done.

The volume of the system increases and a positive amount of work is done.

The volume of the system decreases and a negative amount of work is done.

The volume of the system remains constant and no work is done

Answer 1

As , we know according to first law of thermodynamics--

∆U = ∆W + ∆Q

given--- ∆U = +16J , ∆Q = -14J

the sign of ∆Q is - as heat is released....

so , put values in above law to find ∆W=∆U - ∆Q

= 16-(-14)

= 30J

clearly work is positive and it is also given by -P(∆V) at constant pressure

where ∆V means ( final volume - initial volume of the gas )

clearly work is positive hence -P(∆V) can be only positive if ∆V is negative...

which means (final volume of gas) < (initial volume of gas )

hence , volume of gas decreases and positive work is done....