Question

The molar heat capacity of water at constant pressure, $C$, is $75\, JK ^{-1}\, mol ^{-1}$. When $1.0\, KJ$ of heat is supplied to $100\, g$ of water which is free to expand, the increase in temperature of water is :

• A. 6.6 K
• B. 1.2 K
• C. 2.4 K
• D. 4.8 K

Answer 1

The Correct Option is C

To determine the increase in temperature of the water, we can use the formula for heat transfer at constant pressure:

q = nC\Delta T

Where:

• q is the heat supplied.
• n is the number of moles of the substance.
• C is the molar heat capacity at constant pressure.
• \Delta T is the change in temperature.

Given:

• Heat supplied, q = 1.0\, \text{KJ} = 1000\, \text{J}
• Molar heat capacity of water, C = 75\, \text{JK}^{-1}\,\text{mol}^{-1}
• Mass of water, m = 100\, \text{g}

First, we need to find the number of moles of water, n:

We know the molar mass of water is approximately 18\, \text{g/mol}.

So, the number of moles n is given by:

n = \frac{m}{\text{Molar mass}} = \frac{100}{18} \approx 5.56\, \text{mol}

Substituting the values into the heat transfer equation:

1000 = 5.56 \times 75 \times \Delta T

\Delta T = \frac{1000}{5.56 \times 75}

\Delta T = \frac{1000}{417} \approx 2.4\, \text{K}

Therefore, the increase in temperature of the water is 2.4 K.