PLS HELP ON THIS THERMODYNAMIC QUESTION.....

MULTIPLE CHOICE QUESTION

AN IDEAL GAS IS HEATED AT CONSTANT PRESSURE AND ABSORBS 'Q' AMOUNT OF HEAT. IF Cp/ Cv = GAMMA (y) ...

THEN

(1) INCREASE IN INTERNAL ENERGY IS Q/ y

(2) WORKDONE BY THE GAS IS Q(1-1/y)

(3) INCREASE IN INTERNAL ENERGY IS Q(1-1/y)

(4) WORKDONE BY THE GAS IS Q/y

PLS HELP URGENTLY ...

RATES ASSURED....

Let's break down the problem involving an ideal gas that is heated at constant pressure and absorbs a heat amount of 'Q'. The relationship between the specific heat capacities at constant pressure (Cp) and constant volume (Cv) is given by the ratio γ (gamma), where γ = Cp/Cv. To analyze the situation, we can use the first law of thermodynamics and the definitions of work and internal energy changes.

Understanding the Concepts

When an ideal gas is heated at constant pressure, the heat added to the system can be expressed as:

• Q = ΔU + W

Here, ΔU represents the change in internal energy, and W is the work done by the gas. At constant pressure, the work done by the gas can be defined as:

• W = PΔV

For an ideal gas, the relationship between heat, internal energy, and work can be further analyzed using the specific heat capacities:

• ΔU = nCvΔT
• Q = nCpΔT

Deriving the Relationships

Since we know that:

• γ = Cp/Cv

We can express Cp in terms of Cv:

• Cp = γCv

Substituting this into the equation for Q gives:

• Q = n(γCv)ΔT

Now, we can relate ΔU and W. From the first law of thermodynamics, we can rearrange the equation:

• ΔU = Q - W

At constant pressure, the work done by the gas can also be expressed in terms of the change in temperature:

• W = PΔV = nRΔT

Using the ideal gas law, we can relate ΔV to ΔT:

• ΔV = nRΔT/P

Finding the Answers

Now, let's analyze the options provided:

1. Increase in internal energy is Q/y
2. Work done by the gas is Q(1-1/y)
3. Increase in internal energy is Q(1-1/y)
4. Work done by the gas is Q/y

From our earlier derivations, we can find:

• ΔU = nCvΔT = Q(1 - 1/γ)
• W = Q(1 - 1/γ)

Thus, the correct relationships are:

• ΔU = Q(1 - 1/γ) (which corresponds to option 3)
• W = Q(1 - 1/γ) (which corresponds to option 2)

Final Thoughts

In summary, the correct answers to your multiple-choice question are:

• Increase in internal energy is Q(1 - 1/y) (Option 3)
• Work done by the gas is Q(1 - 1/y) (Option 2)

Understanding these relationships is crucial in thermodynamics, as they help us analyze how energy is transferred and transformed in systems involving gases. If you have any further questions or need clarification on any of these concepts, feel free to ask!