Explanation

Explanation

Explanation

Explanation

The degrees of freedom refer to the number of independent ways a gas molecule can store energy.

For a monoatomic gas (e.g., noble gases like helium, neon, argon):

• It has only translational motion along the x, y, and z axes.
• There are no rotational or vibrational degrees of freedom.

Thus, the total degrees of freedom for a monoatomic gas is 3 (one for each spatial direction: x, y, and z).

Explanation

Given:

Initial efficiency (η₁) = 50% = 0.5

Initial cold body temperature (T₁) = 17°C = 290 K

Initial hot body temperature (T₂) = unknown

We know that the efficiency of a Carnot engine is:

η = 1 - (T₁ / T₂)

0.5 = 1 - (290 K / T₂)

T₂ = 580 K

Now, the hot body temperature is increased by 145°C:

New hot body temperature (T₂') = 580 K + 145°C = 725 K

New efficiency (η₂) is:

η₂ = 1 - (T₁ / T₂')

= 1 - (290 K / 725 K)

≈ 0.6

New efficiency (η₂) is approximately 60%.

Explanation

Explanation

Explanation

Explanation

Explanation

Let's denote the weight of the man in the stationary lift as W and the weight in the accelerating lift as W'.

We know that W' / W = 2/3.

When the lift is accelerating downward with acceleration 'a', the apparent weight (W') is given by:

W' = W - ma

where m is the mass of the man.

Since W' / W = 2/3, we can write:

(W - ma) / W = 2/3

Substitute W = mg (where g is the acceleration due to gravity):

(mg - ma) / mg = 2/3

Simplify:

g - a = (2/3)g

a = g - (2/3)g

a = (1/3)g

a = g/3