Thermal Properties Of Matter

The correct answer is (B) : 590 g
As of steam at melts of ice at
of steam will melt of ice at
Water in calorimeter

The correct answer is (C) :

= constant for all scales

Given:

The elongation in the wire is given by the formula:

Where:

• is the force applied on the wire,
• is the length of the wire,
• is the cross-sectional area of the wire,
• is the Young's modulus of the wire material.

Substitute the values into the elongation formula:

Simplifying the expression:

The correct option is (C) 28°C






= 28°C

Solution:
We will use Newton's Law of Cooling. $ T t T_s k 80^{\circ}C 60^{\circ}C T_1 = 80^{\circ}C T_2 = 60^{\circ}C t_1 = 5 \text{ minutes} = 300 \text{ seconds} T_s = 20^{\circ}C 60^{\circ}C 40^{\circ}C T_1 = 60^{\circ}C T_2 = 40^{\circ}C t_2 T_s = 20^{\circ}C 60^{\circ}C 40^{\circ}C$ is 500 seconds.

The correct answer is (1) 500 s.

Calculation Using Wien’s Displacement Law:

Step 1: Formula

According to Wien’s displacement law:

or equivalently:

Thus, for two states:

Step 2: Given Data

• Initial temperature:
• Initial wavelength:
• Temperature increase:
• Final temperature:

Step 3: Calculate New Wavelength

From the formula :

Substitute the values:

Simplify:

Conclusion:

The new wavelength corresponding to the maximum intensity is .

Answer: A

Given:

The heat passing through the cross-section of the rod is:

Step-by-Step Solution:

1. Heat Current:

The heat current ( ) is the rate of change of with respect to time:

2. Condition for Minimum Heat Current:

To find the time at which the heat current is minimum, differentiate again: Set to find the critical point:

3. Minimum Heat Current:

Substitute into the expression for : Simplify each term: Combine terms:

Final Answer:

The correct answer is (B): .

Use the Temperature-Resistance Relationship for a Platinum Resistance Thermometer:
The resistance of a platinum resistance thermometer at a temperature (in °C) is given by:
where:
is the resistance at 0°C (ice point),
is the temperature coefficient of resistance of platinum,
is the temperature difference from the ice point.

Given Data:
(resistance at 0°C)
(resistance at 100°C)
Temperature of the hot bath:

Calculate the Temperature Coefficient :
Using the resistance values at 0°C and 100°C:

Substitute and :

Calculate the Resistance at 400°C:
Now, using :

Substitute and :

Conclusion:
The resistance of the platinum wire at 400°C is .

To determine the extension in length of the wire, we apply the formula from Hooke's Law relating stress, strain, and Young’s modulus: , where and is Young’s Modulus.

1. Convert the area from to :
   .
2. Calculate the stress on the wire:
   .
3. The strain in the wire is given by:
   .
4. Calculate the extension using :
   .
5. Convert the extension into micrometers ( ):
   .
6. Verify the calculated extension is within the specified range (20,20), confirming the accuracy of our computation.

Therefore, the wire will extend in length by 20 μm, fitting perfectly within the expected range.

Given:

where is the spring constant and is the natural length of the spring.

To find the tension for the length , we use:

Substituting the values of and from the given equations:

Conclusion:
Hence, the value of the tension is .