How Many Kilograms Of Nitrogen Boil Away By The Time The Copper Reaches 77.3 K?(The Specific Heat Of Copper Is 0.0920 Cal/g°C, And The Latent Heat Of Vaporization Of Nitrogen Is 48.0 Cal/g.)In An Insulated Vessel, 250 G Of Ice At 0°C Is Added To 600 G

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In this article, we will delve into a fascinating physics problem that involves the concept of heat transfer, specific heat capacity, and latent heat of vaporization. The problem is as follows: how many kilograms of nitrogen boil away by the time the copper reaches 77.3 K? To solve this problem, we need to understand the given parameters and the underlying physics.

Given Parameters

  • The specific heat of copper is 0.0920 cal/g°C.
  • The latent heat of vaporization of nitrogen is 48.0 cal/g.
  • The initial temperature of the copper is not specified, but we can assume it is at room temperature, which is approximately 20°C.
  • The initial mass of the copper is not specified, but we can assume it is a small amount, so we can neglect its heat capacity compared to the heat capacity of the nitrogen.
  • The initial temperature of the nitrogen is also not specified, but we can assume it is at room temperature, which is approximately 20°C.

The Physics Behind the Problem

When the copper is heated, it will transfer heat to the nitrogen, causing it to boil. The heat transfer occurs due to the temperature difference between the copper and the nitrogen. As the copper heats up, it will lose heat to the nitrogen, causing the nitrogen to boil.

The Heat Transfer Equation

The heat transfer equation is given by:

Q = mcΔT

where Q is the heat transferred, m is the mass of the copper, c is the specific heat capacity of the copper, and ΔT is the temperature difference between the copper and the nitrogen.

The Latent Heat of Vaporization

The latent heat of vaporization of nitrogen is given by:

L = 48.0 cal/g

This means that 48.0 calories of heat are required to vaporize 1 gram of nitrogen.

The Boiling Point of Nitrogen

The boiling point of nitrogen is 77.3 K. This means that at this temperature, the nitrogen will boil and turn into a gas.

The Problem: How Many Kilograms of Nitrogen Boil Away?

Now that we have understood the problem and the underlying physics, let's solve it. We need to find out how many kilograms of nitrogen boil away by the time the copper reaches 77.3 K.

Step 1: Calculate the Heat Transferred to the Nitrogen

To calculate the heat transferred to the nitrogen, we need to use the heat transfer equation:

Q = mcΔT

We know that the specific heat capacity of copper is 0.0920 cal/g°C, and the initial temperature of the copper is 20°C. We also know that the boiling point of nitrogen is 77.3 K, which is equivalent to -195.8°C.

Let's assume that the copper heats up to 77.3 K, which is equivalent to -195.8°C. The temperature difference between the copper and the nitrogen is:

ΔT = 20°C - (-195.8°C) = 215.8°C

Now, we can calculate the heat transferred to the nitrogen:

Q = mcΔT = 250 g x 0.0920 cal/g°C x 215.8°C = 4991.4 cal

Step 2: Calculate the Mass of Nitrogen that Boils Away

Now that we have calculated the heat transferred to the nitrogen, we can calculate the mass of nitrogen that boils away. We know that the latent heat of vaporization of nitrogen is 48.0 cal/g.

Let's assume that the heat transferred to the nitrogen is used to vaporize a certain mass of nitrogen. We can set up the following equation:

Q = mL

where Q is the heat transferred, m is the mass of nitrogen that boils away, and L is the latent heat of vaporization of nitrogen.

We know that the heat transferred to the nitrogen is 4991.4 cal, and the latent heat of vaporization of nitrogen is 48.0 cal/g. We can solve for the mass of nitrogen that boils away:

m = Q / L = 4991.4 cal / 48.0 cal/g = 103.9 g

Conclusion

In this article, we have solved a fascinating physics problem that involves the concept of heat transfer, specific heat capacity, and latent heat of vaporization. We have calculated the heat transferred to the nitrogen and used it to find the mass of nitrogen that boils away by the time the copper reaches 77.3 K. The answer is approximately 103.9 grams.

References

  • [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
  • [2] Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.

Additional Resources

In our previous article, we delved into a fascinating physics problem that involved the concept of heat transfer, specific heat capacity, and latent heat of vaporization. We calculated the heat transferred to the nitrogen and used it to find the mass of nitrogen that boils away by the time the copper reaches 77.3 K. In this article, we will answer some frequently asked questions related to the problem.

Q: What is the specific heat capacity of copper?

A: The specific heat capacity of copper is 0.0920 cal/g°C.

Q: What is the latent heat of vaporization of nitrogen?

A: The latent heat of vaporization of nitrogen is 48.0 cal/g.

Q: What is the boiling point of nitrogen?

A: The boiling point of nitrogen is 77.3 K, which is equivalent to -195.8°C.

Q: How much heat is transferred to the nitrogen?

A: The heat transferred to the nitrogen is 4991.4 cal.

Q: How much nitrogen boils away by the time the copper reaches 77.3 K?

A: The mass of nitrogen that boils away by the time the copper reaches 77.3 K is approximately 103.9 grams.

Q: What is the temperature difference between the copper and the nitrogen?

A: The temperature difference between the copper and the nitrogen is 215.8°C.

Q: How is the heat transfer equation used to solve the problem?

A: The heat transfer equation is used to calculate the heat transferred to the nitrogen. The equation is:

Q = mcΔT

where Q is the heat transferred, m is the mass of the copper, c is the specific heat capacity of the copper, and ΔT is the temperature difference between the copper and the nitrogen.

Q: What is the significance of the latent heat of vaporization of nitrogen?

A: The latent heat of vaporization of nitrogen is the amount of heat required to vaporize 1 gram of nitrogen. In this problem, it is used to calculate the mass of nitrogen that boils away by the time the copper reaches 77.3 K.

Q: How is the mass of nitrogen that boils away calculated?

A: The mass of nitrogen that boils away is calculated using the following equation:

m = Q / L

where m is the mass of nitrogen that boils away, Q is the heat transferred to the nitrogen, and L is the latent heat of vaporization of nitrogen.

Q: What is the relationship between the heat transferred to the nitrogen and the mass of nitrogen that boils away?

A: The heat transferred to the nitrogen is directly proportional to the mass of nitrogen that boils away. This is because the latent heat of vaporization of nitrogen is a constant value, and the heat transferred to the nitrogen is used to vaporize the nitrogen.

Conclusion

In this article, we have answered some frequently asked questions related to the physics problem we solved in our previous article. We have explained the concept of heat transfer, specific heat capacity, and latent heat of vaporization, and how they are used to solve the problem. We hope this article has provided a better understanding of the physics behind the problem.

References

  • [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
  • [2] Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.

Additional Resources