Steam at $100^{\circ} \mathrm{C}$ is passed into $1 \mathrm{~kg}$ of water contained in a calorimeter at…

Steam at $100^{\circ} \mathrm{C}$ is passed into $1 \mathrm{~kg}$ of water contained in a calorimeter at $9^{\circ} \mathrm{C}$ till the temperature of water and calorimeter is increased to $90^{\circ} \mathrm{C}$. The mass of the steam condensed is nearly (water equivalent of calorimeter $=0.1 \mathrm{~kg}$, specific heat of water $=1 \mathrm{calg}^{-1}{ }^{\circ} \mathrm{C}^{-1}$ and latent heat of vaporisation $=540 \mathrm{calg}^{-1}$ )
  1. $81 \mathrm{~g}$
  2. $162 \mathrm{~g}$
  3. $243 \mathrm{~g}$
  4. $486 \mathrm{~g}$

Solution

Let mass of the steam condensed is $x$. Heat released $=$ Heat gained by water $ \begin{aligned} & \Rightarrow x \times 540+x \times 1 \times(100-90) \\ & \quad=1 \times 1 \times(90-9)+0.1 \times 1 \times(90-9) \\ & \Rightarrow 540 x+10 x=81+81 \\ & \Rightarrow \quad x=\frac{891}{550}=0 \cdot 162 \mathrm{~kg}, x=162 \mathrm{~g} \end{aligned} $

Asked in: AP EAMCET 2018 (22 Apr Shift 1)

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