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: Understanding the Concept:
Heat generated by slippage during clutch engagement is absorbed by the pressure plate and flywheel elements, causing a transient temperature rise.

Step 2: Key Formula or Approach:
The heat absorbed \(Q\) by a substance is related to its temperature rise by:
\[ Q = m \cdot c \cdot \Delta T \] where:
\(m\) = mass of absorbing elements
\(c\) = specific heat
\(\Delta T\) = change in temperature (\(T_{\text{after}} - T_{\text{before}}\))

Step 3: Detailed Explanation:
Identify and substitute the given values:
- Mass (\(m\)) = \(10\text{ kg}\)
- Initial temperature = \(50 ^\circ\text{C}\)
- Final temperature = \(200 ^\circ\text{C}\)
Calculate the temperature rise (\(\Delta T\)):
\[ \Delta T = 200 - 50 = 150 ^\circ\text{C} \] Substitute into the thermal balance equation:
\[ Q = 10 \times c \times 150 \] \[ Q = 1500 \cdot c \] Rearranging for specific heat \(c\):
\[ c = \frac{Q}{1500} \]

Step 4: Final Answer:
The correct option is 2, which corresponds to \(\frac{Q}{1500}\).