Question

Assertion (A): When \(1\,g\) of ice melts at constant temperature at a pressure of \(1\,atm\), the increase in internal energy is greater than \(80\,cal\).
Reason (R): During melting of ice, work is done on the ice.

• A. Both A and R are true. R is the correct explanation of A
• B. Both A and R are true, but R is not the correct explanation of A
• C. A is true, R is false
• D. A is false, R is true

Hint:

Use sign convention carefully: \[ Q=\Delta U+W \] where \(W\) is work done by the system.

Answer 1

The Correct Option is A

Step 1: Bring in the first law.
The first law of thermodynamics links heat, internal energy and work. \[ Q = \Delta U + W \] Here $Q$ is heat added, $\Delta U$ is the rise in internal energy, and $W$ is work done by the system.

Step 2: Heat needed to melt the ice.
Melting $1$ g of ice needs the latent heat. \[ Q = 80\,\text{cal} \]
Step 3: Think about the volume change.
Ice is less dense than water, so when ice melts it actually shrinks in volume. The surroundings push in as it shrinks.
Step 4: Decide the sign of work.
Since the volume goes down, the system does negative work, meaning work is done on the ice. \[ W < 0 \]
Step 5: Find the internal energy change.
Rearranging the first law, \[ \Delta U = Q - W \] With $W$ negative, we subtract a negative, which makes $\Delta U$ larger than $Q$. \[ \Delta U > 80\,\text{cal} \]
Step 6: Judge the statements.
So the increase in internal energy is more than $80$ cal, and the reason that work is done on the ice correctly explains this. Both A and R are true and R explains A. \[ \boxed{\text{Both A and R true, R explains A}} \]