Density of water at and are and respectively. The increase in internal energy of of water when it is heated from to is ________ J. (Specific heat capacity of water = 4.2 J/kg, and 1 atmospheric pressure = ) [2026]

Question

Density of water at $4 ° C$ and $20 ° C$ are $1000 {kg/m}^{3}$ and $998 {kg/m}^{3}$ respectively. The increase in internal energy of $4 kg$ of water when it is heated from $4 ° C$ to $20 ° C$ is ________ J.

(Specific heat capacity of water = 4.2 J/kg, and 1 atmospheric pressure = $10^{5} Pa$ ) [2026]

Smart Achievers · Accepted Answer

(4)

$Q = m s Δ T = 4 \times 4200 \times 16 J = 268800 J$

$W = P Δ V$

$Δ V = (\frac{m}{ρ_{f}} - \frac{m}{ρ_{i}}) = 4 [\frac{1}{998} - \frac{1}{1000}]$

$P = 10^{5} Pa$

$∴$ $W = 10^{5} \times 4 [\frac{1}{998} - \frac{1}{1000}] = \frac{8 \times 10^{5}}{10^{3} \times 998} \approx 0.8 J$

$Δ U = Q - W = 268799.2 J$

Solution

1 315826.2

2 234699.2

3 258700.8

4 268799.2

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