Question

A calorimeter contains 10 g of water at $20^{\circ}C$. The temperature falls to $15^{\circ}C$ in 10 min. When calorimeter contains 20 g of water at $20^{\circ}C$, it takes 15 min. for the temperature to become $15^{\circ}C$. The water equivalent of the calorimeter is}

• A. 50 g
• B. 25 g
• C. 10 g
• D. 5 g

Hint:

Rate of heat loss depends on the surface area and temperature difference, not the mass of liquid.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The rate of heat loss is assumed to be constant for the same temperature difference.

Step 2: Key Formula or Approach:
Heat loss \( \Delta Q = (m + w) c \Delta T \).
Rate of heat loss \( R = \frac{\Delta Q}{t} \).

Step 3: Detailed Explanation:
Since the temperature range (\( 20 \rightarrow 15 \)) is the same, \( R_1 = R_2 \).
\[ \frac{(10 + w) \times c \times 5}{10} = \frac{(20 + w) \times c \times 5}{15} \]
Cancelling common factors (\( 5c \)):
\[ \frac{10 + w}{10} = \frac{20 + w}{15} \]
Multiply both sides by 30:
\[ 3(10 + w) = 2(20 + w) \]
\[ 30 + 3w = 40 + 2w \implies w = 10 \text{ g} \]

Step 4: Final Answer:
The water equivalent is 10 g.