Question

$\Delta E$ is always positive when :

• A. system absorbs heat and work is done on it
• B. system emits heat and work is done on it
• C. system emits heat and no work is done on it
• D. system absorbs heat and work is done by it

Answer 1

Answer: (A)

system absorbs heat and work is done on it

Answer 2

The question asks for the condition under which the change in internal energy ($\Delta E$) is always positive. This involves applying the First Law of Thermodynamics, which states:

$\Delta E = Q + W$

Where:

• $\Delta E$ is the change in internal energy of the system.
• $Q$ is the heat exchanged by the system.
• $W$ is the work done on or by the system.

We use the standard sign conventions:

• $Q > 0$ if heat is absorbed by the system.
• $Q < 0$ if heat is emitted by the system.
• $W > 0$ if work is done on the system.
• $W < 0$ if work is done by the system.

Let's analyze each option:

1. System absorbs heat and work is done on it:

   • System absorbs heat: $Q > 0$
   • Work is done on it: $W > 0$
   • In this case, $\Delta E = (\text{positive value}) + (\text{positive value})$. The sum of two positive values is always positive.
   • Therefore, $\Delta E$ is always positive.

2. System emits heat and work is done on it:

   • System emits heat: $Q < 0$
   • Work is done on it: $W > 0$
   • In this case, $\Delta E = (\text{negative value}) + (\text{positive value})$. The sign of $\Delta E$ depends on the magnitudes of $Q$ and $W$. If $|W| > |Q|$, $\Delta E$ will be positive. If $|W| < |Q|$, $\Delta E$ will be negative. If $|W| = |Q|$, $\Delta E$ will be zero. So, $\Delta E$ is not always positive.

3. System emits heat and no work is done on it:

   • System emits heat: $Q < 0$
   • No work is done: $W = 0$
   • In this case, $\Delta E = Q + 0 = Q$. Since $Q < 0$, $\Delta E$ will always be negative.

4. System absorbs heat and work is done by it:

   • System absorbs heat: $Q > 0$
   • Work is done by it: $W < 0$
   • In this case, $\Delta E = (\text{positive value}) + (\text{negative value})$. The sign of $\Delta E$ depends on the magnitudes of $Q$ and $W$. If $|Q| > |W|$, $\Delta E$ will be positive. If $|Q| < |W|$, $\Delta E$ will be negative. If $|Q| = |W|$, $\Delta E$ will be zero. So, $\Delta E$ is not always positive.

Based on the analysis, only when the system absorbs heat and work is done on it, $\Delta E$ is always positive.