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`

Step-by-step explanation:

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

`PV=nRT`

or,

`PV=(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* V=(2610g)/(18g/mol)* 8.31\text{L kPa }* 473K\\\\V=2849.7L`

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

`1m^3=1000L`

So,
`\Rightarrow (1m^3)/(1000L)* 2849.7L`

`\Rightarrow 2.8497m^3`

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