Question

Liquid water at 25°C and 1 bar fills a rigid vessel. If heat is added to the water until its temperature reaches 50°C, what pressure is developed? The average value of β between 25 and 50°C is 36.2 × 10−5K−1. The value of κ at 1 bar and 50°C is 4.42 × 10−5bar−1, and may be assumed to be independent of P. The specific volume of liquid water at 25°C is 1.0030 cm3·g−1

Answer 1

Answer:

The developed pressure is 205.75 bar.

Explanation:

Given that,

Temperature of water =25°C = 273+25 = 298 K

Pressure = 1 bar

Increases temperature = 50°C = 273+50 = 323 K

Value of $\beta = 36.2\times10^{-5}\ K^{-1}$

Value of $k=4.42\times10^{-5}\ bar^{-1}$

Specific volume of liquid = 1.0030 cm³/g

We need to calculate the final pressure

Using formula for constant volume change

$\beta(T_{2}-T)_{1})-k(P_{2}-P_{1})=0$

Put the value into the formula

$36.2\times10^{-5}(323-298)-4.42\times10^{-5}(P_{2}-1)=0$

$P_{2}=\dfrac{36.2\times10^{-5}(323-298)}{4.42\times10^{-5}}+1$

$P_{2}=205.75\ bar$

Hence, The developed pressure is 205.75 bar.