To determine the effectiveness of a balanced counter flow heat exchanger, we need to use the concept of the Number of Transfer Units (NTU). The NTU is a dimensionless parameter that represents the heat transfer capacity of the heat exchanger.

Given that Mh Ch = McCc, where Mh and Ch are the mass flow rate and specific heat of the hot fluid, and Mc and Cc are the mass flow rate and specific heat of the cold fluid, we can assume that the heat capacity rates of both fluids are equal.

The NTU is calculated using the formula:

NTU = (UA)/(Mh * Ch)

where U is the overall heat transfer coefficient and A is the heat transfer surface area.

In a balanced counter flow heat exchanger, the effectiveness (ε) is given by the equation:

ε = (1 - exp(-NTU))/(1 - exp(-NTU * (Cc/Ch)))

Given that NTU = 1.0 in this case, we can substitute this value into the equation to find the effectiveness.

ε = (1 - exp(-1))/(1 - exp(-1 * (Cc/Ch)))

Since the heat capacity rates of both fluids are equal, Cc/Ch = 1.

ε = (1 - exp(-1))/(1 - exp(-1 * 1))
= (1 - 0.368)/(1 - 0.368)
= 0.632/0.632
= 1

Therefore, the effectiveness of the heat exchanger is 1.

Explanation:
- To determine the effectiveness of the heat exchanger, we need to calculate the NTU using the given formula.
- The effectiveness equation is then used to calculate the effectiveness using the NTU value.
- Since the NTU is equal to 1.0 and the heat capacity rates of both fluids are equal, the effectiveness is equal to 1.
- This indicates that the heat exchanger is able to transfer all of the available heat from the hot fluid to the cold fluid, resulting in maximum heat transfer efficiency.