Question

2.61 kilograms of water in a container have a pressure of 200 kPa and temperature of 200°C . What is the volume of this container? m (Round to three decimal places)

Answer 1

Answer: The volume of the container is $2.8497m^3$

Explanation:

To calculate the volume of water, we use the equation given by ideal gas, which is:

$PV=nRT$

or,

$PV=\frac{m}{M}RT$

where,

P = pressure of container = 200 kPa

V = volume of container = ? L

m = Given mass of water = 2.61 kg = 2610 g   (Conversion factor: 1kg = 1000 g)

M = Molar mass of water = 18 g/mol

R = Gas constant = $8.31\text{L kPa }mol^{-1}K^{-1}$

T = temperature of container = $200^oC=[200+273]K=473K$

Putting values in above equation, we get:

$200kPa\times V=\frac{2610g}{18g/mol}\times 8.31\text{L kPa }\times 473K\\\\V=2849.7L$

Converting this into cubic meter, we use the conversion factor:

$1m^3=1000L$

So, $\Rightarrow \frac{1m^3}{1000L}\times 2849.7L$

$\Rightarrow 2.8497m^3$

Hence, the volume of the container is $2.8497m^3$