Question

Consider the process for steam in a cylinder shown below. Suppose the change in the internal energy in this process is 24 kJ. Find the heat entering the system (in J).

Answer 1

The heat entering the system for a change in internal energy of 24 kJ is 24000 J.

Step-by-step explanation:

The relationship between heat, work, and internal energy change is given by the first law of thermodynamics: ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat entering the system, and W is the work done by the system. Given ΔU = 24 kJ (which is 24000 J when converted to joules), and assuming there is no work done (W = 0, or it's not given), we can rearrange the equation to solve for Q.

ΔU = Q - W can be simplified to Q = ΔU + W. Since work (W) is assumed to be zero or not given, the equation becomes Q = ΔU. Therefore, Q (heat entering the system) equals the change in internal energy, which in this case is 24000 J. This implies that the heat entering the system is directly related to the change in internal energy and, in this particular scenario, they are numerically equal.

Answer 2

To determine the heat entering the system, we need to know both the change in internal energy and the work done by the system. If only the internal energy change is known, additional information about work is required to calculate the heat transfer accurately.

Step-by-step explanation:

Calculating Heat Transfer in a Thermodynamic Process

To find the heat entering the system, we use the first law of thermodynamics, which states that the change in internal energy of a system (ΔU) is equal to the heat transfer to the system (Q) minus the work done by the system (W):

ΔU = Q - W

In this case, we are told the change in the internal energy (ΔU) is 24 kJ. However, we do not have information about the work done by the system. Assuming we have this information, we can rearrange the equation to solve for heat transfer (Q):

Q = ΔU + W

Once we have the value for W, we can insert it along with the given ΔU to find Q. Remember to ensure that all the units are consistent when performing the calculation. If W is not specified, Q cannot be determined solely from the given ΔU.