an experiment, a 0.280-kg piece of ceramic superconducting material at 23 °C is placed in liquid nitrogen at its boiling point (−195.8 °C) to cool. The nitrogen is in a perfectly insulated flask that allows the gaseous N2 to escape immediately. How much mass of liquid nitrogen will be boiled away? (Take the specific heat of the ceramic material to be the same as that of glass.)
This is worked almost the same as the Al/Cu problem above.
heat lost by ceramic on cooling is
q = mass ceramic x specific heat ceramic x (Tfinal-Tinitial)
Then look up heat vaporization liquid nitrogen.
joules lost by ceramic = mass N2 x heat vaporization liquid N2. Solve for mass N2.
To find the mass of liquid nitrogen that will be boiled away, we need to determine the heat transferred from the ceramic material to the liquid nitrogen.
The heat transferred can be calculated using the equation:
Q = mcΔT
Where:
Q is the heat transferred
m is the mass
c is the specific heat capacity
ΔT is the change in temperature
First, let's calculate the heat transferred from the ceramic material to the liquid nitrogen.
Given:
Mass of the ceramic material (m1) = 0.280 kg
Temperature of the ceramic material (T1) = 23 °C
Temperature of the liquid nitrogen (T2) = -195.8 °C (boiling point of liquid nitrogen)
Next, we need to calculate the change in temperature (ΔT) of the ceramic material:
ΔT = T2 - T1
ΔT = (-195.8 °C) - (23 °C)
ΔT = -218.8 °C
Now, we need to determine the specific heat capacity (c) of the ceramic material. Since it is given that the specific heat of the ceramic material is the same as that of glass, we can use the specific heat capacity of glass.
Specific heat capacity of glass (c) = 840 J/kg°C
Now, we can calculate the heat transferred:
Q = mcΔT
Q = (0.280 kg)(840 J/kg°C)(-218.8 °C)
By calculating Q, we will get the heat transferred from the ceramic material to the liquid nitrogen.
Please note that the specific heat capacity provided is in J/kg°C, so the resulting heat transferred will be in Joules.
Is there anything else you would like to know?
To calculate the mass of liquid nitrogen that will be boiled away, we can use the heat transfer equation:
Q = mcΔT
Where:
Q is the heat transferred,
m is the mass of the substance,
c is the specific heat capacity of the substance, and
ΔT is the change in temperature.
In this case, we need to calculate the heat transferred from the ceramic material to the liquid nitrogen.
First, let's calculate the heat transferred from the ceramic material:
Q1 = mcΔT1
Where:
m = 0.280 kg (mass of ceramic material),
c = specific heat capacity of glass (we'll assume it to be 840 J/kg°C, similar to glass), and
ΔT1 = (23 °C - (-195.8 °C)) = 218.8 °C.
Q1 = (0.280 kg)(840 J/kg°C)(218.8 °C)
Q1 = 53160 J
Next, let's calculate the heat transferred to boil away the liquid nitrogen:
Q2 = mL
Where:
m = mass of liquid nitrogen to be boiled away (we need to find this),
L = latent heat of vaporization of liquid nitrogen (we'll assume it to be 200 kJ/kg or 200000 J/kg.
Q2 = mL
Now, the total heat transferred should be zero since the process is perfectly insulated:
Q1 + Q2 = 0
Q2 = -Q1
Substituting the known values:
(-Q1) = mL
(-53160 J) = m(200000 J/kg)
m = (-53160 J) / (200000 J/kg)
Calculating this, we find:
m ≈ -0.266 kg
Since mass cannot be negative, we take the absolute value:
m ≈ 0.266 kg
Therefore, approximately 0.266 kg of liquid nitrogen will be boiled away during the experiment.