Question

The bulk temperature reached by the heat absorbing elements of a clutch after and before engagement are 200 \(^\circ\text{C}\) and 50 \(^\circ\text{C}\) respectively. The total mass of the heat absorbing elements is 10 kg. If "Q" joules of heat is generated in the clutch, required specific heat of heat-absorbing elements (in \(\text{J}\cdot\text{kg}^{-1}\cdot^\circ\text{C}^{-1}\)) will be

• A. 10Q150
• B. Q1500
• C. 10Q250
• D. Q2500

Hint:

Always simplify product coefficients first:
\(10\text{ kg} \times 150 ^\circ\text{C} = 1500\text{ kg}\cdot^\circ\text{C}\).
Since \(Q = 1500c\), specific heat \(c\) must have 1500 in the denominator.

Answer 1

The Correct Option is B

Step 1: Set up the heat balance for the clutch elements.
All the frictional heat generated during clutch engagement, Q joules, is absorbed by the heat absorbing elements and raises their temperature, so \( Q = m \, c \, \Delta T \), where m is the mass of the absorbing elements and c is their specific heat.
Step 2: Insert the known temperature rise and mass.
The temperature rises from 50 C to 200 C, giving \( \Delta T = 150 \ ^\circ C \), and the mass is given as \( m = 10 \text{kg} \), so \( Q = 10 \times c \times 150 = 1500 \, c \).
Step 3: Solve for specific heat.
Rearranging gives \( c = \dfrac{Q}{1500} \), which in the option's notation is written as Q1500.
\[ \boxed{Q1500} \]