Question

In a system, \(x\,\mathrm{J}\) of heat is absorbed and \(y\,\mathrm{J}\) of work is done by the system. What is \(\Delta U\) (in kJ)?

• A. \((x-y)\times10^{-3}\)
• B. \((x+y)\)
• C. \((x-y)\times10^{3}\)
• D. \(\dfrac{x}{y}\times10^{-3}\)

Hint:

First law of thermodynamics: \[ \boxed{ \Delta U=q-w } \] where \(q\) is positive when heat is absorbed and \(w\) is positive when work is done by the system.

Answer 1

The Correct Option is A

Step 1: Apply the first law of thermodynamics. The first law states, \[ \Delta U=q-w, \] where \[ q=x\ \mathrm{J} \] is the heat absorbed and \[ w=y\ \mathrm{J} \] is the work done by the system. Thus, \[ \Delta U=x-y\ \mathrm{J}. \]

Step 2: Convert joules to kilojoules. Since \[ 1\,\mathrm{kJ}=10^3\,\mathrm{J}, \] \[ \Delta U = \frac{x-y}{1000} = (x-y)\times10^{-3}\ \mathrm{kJ}. \] Hence, \[ \boxed{(x-y)\times10^{-3}\ \mathrm{kJ}} \] Therefore, \[ \boxed{(A)} \] is the correct answer.