Final answer:
To calculate the specific volume of water at a given state, we use the ideal gas equation. The specific volume can be calculated by dividing the volume by the mass of the substance. For the given state of water at 300 kPa and 260 degrees Celsius, the specific volume is approximately 0.0601 m³/kg.
Step-by-step explanation:
To calculate the specific volume of water at a given state, we need to use the ideal gas equation. The specific volume (v) is defined as the volume (V) divided by the mass (m) of the substance. The ideal gas equation is:
P · V = m · R · T
Where P is the pressure, V is the volume, m is the mass, R is the gas constant, and T is the temperature.
Given that the water is at a pressure of 300 kPa and a temperature of 260 degrees Celsius, we can convert the temperature to Kelvin by adding 273.15. So, T = 260 + 273.15 = 533.15 K.
Next, we need to find the molar mass of water. The molar mass (M) of water is 18.0 g/mol. Since we are looking for the specific volume, we need to convert the given pressure to Pascal by multiplying it by 1000 to get 300,000 Pa.
Now, we can rearrange the ideal gas equation to solve for the specific volume:
v = V/m = (P · V)/(m · R · T)
Plugging in the values, we get:
v = (300,000 Pa · 1 m³)/(1 kg · 8.3145 J/(mol · K) · 533.15 K) ≈ 0.0601 m³/kg
So, the specific volume of water at the given state is approximately 0.0601 m³/kg.