Liquid nitrogen, which has a boiling point of 77 K, is commonly used to cool substances to low temperatures.
How much energy must be removed from
1.4 kg of gaseous nitrogen at 77 K for it to completely liquefy? Assume the latent heat of liquid nitrogen is 2.01 × 105 J/kg.
Answer in units of J
it's 2.01*10^5
Well, that's a chilling question! To determine the amount of energy needed to completely liquefy 1.4 kg of gaseous nitrogen at 77 K, we can use the equation:
Energy = mass × latent heat of liquid nitrogen
Plugging in the values, we get:
Energy = 1.4 kg × 2.01 × 105 J/kg
Calculating that, the answer comes out to be:
Energy = 2.814 × 105 J
So, approximately 281,400 joules of energy must be removed to turn that gaseous nitrogen into a chill liquid.
To determine the energy that must be removed from 1.4 kg of gaseous nitrogen to completely liquefy it, we need to calculate the heat transfer required.
First, let's determine the initial energy content of the gaseous nitrogen. We can use the specific heat capacity of nitrogen gas to calculate this. The specific heat capacity of nitrogen gas (at constant pressure) is approximately 29.1 J/(mol·K).
To convert 1.4 kg of nitrogen to moles, we need to divide the mass by the molar mass of nitrogen, which is approximately 28.01 g/mol.
1.4 kg = 1400 g
Number of moles of nitrogen = 1400 g / 28.01 g/mol ≈ 49.964 mol
Next, we can calculate the initial energy content of the gaseous nitrogen using the specific heat capacity:
Initial energy = Number of moles × Specific heat capacity × Change in temperature
The change in temperature is the difference between the boiling point of nitrogen gas (77 K) and the final temperature when it's completely liquefied, which is 77 K.
Initial energy = 49.964 mol × 29.1 J/(mol·K) × 77 K ≈ 111,845 J
Now, to find the energy that must be removed to completely liquefy the nitrogen, we use the latent heat of liquid nitrogen, which is given as 2.01 × 10^5 J/kg.
Energy required = Mass of nitrogen × Latent heat of liquid nitrogen
Energy required = 1.4 kg × 2.01 × 10^5 J/kg = 281,400 J
Therefore, the energy that must be removed from 1.4 kg of gaseous nitrogen at 77 K for it to completely liquefy is approximately 281,400 J.