A contractor uses a paddle stirrer to mix a can of paint. The paddle turns at 27.4 rad/s and exerts a torque of 15.4 N-m on the paint, doing work on the paint at a rate of Power = TW = 15.4 N•m × 27.4 rad/s = 422.0 W. An internal energy increase of 12.8 kJ causes the temperature of the paint to increase by 1.00 K. If there were no heat flow between the paint and the surroundings, what would be the temperature change of the paint as it is stirred for 5.00 min? |K
A contractor uses a paddle stirrer to mix a can of paint. The paddle turns at 27.4 rad/s and exerts a torque of 15.4 N-m on the paint, doing work on the paint at a rate of Power = TW = 15.4 N•m × 27.4 rad/s = 422.0 W. An internal energy increase of 12.8 kJ causes the temperature of the paint to increase by 1.00 K. If there were no heat flow between the paint and the surroundings, what would be the temperature change of the paint as it is stirred for 5.00 min? |K
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### Mixing Paint and Temperature Change
**Required Information**
A contractor uses a paddle stirrer to mix a can of paint. The paddle turns at a rate of 27.4 rad/s and exerts a torque of 15.4 N·m on the paint. This results in the paddle doing work on the paint at a rate calculated as follows:
- **Power (P)** = τω = 15.4 N·m × 27.4 rad/s = 422.0 W
An internal energy increase of 12.8 kJ causes the temperature of the paint to increase by 1.00 K.
**Problem Statement**
If there were no heat flow between the paint and the surroundings, what would be the temperature change of the paint as it is stirred for 5.00 minutes?
\[\_\_\_\_\_ \text{ K}\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F528734fa-2f56-42f1-ac26-0d1ff4e0efca%2Fc24a0510-b7eb-44e1-9e13-a91e90637bf4%2Fvtlw0m_processed.png&w=3840&q=75)
Transcribed Image Text:### Mixing Paint and Temperature Change
**Required Information**
A contractor uses a paddle stirrer to mix a can of paint. The paddle turns at a rate of 27.4 rad/s and exerts a torque of 15.4 N·m on the paint. This results in the paddle doing work on the paint at a rate calculated as follows:
- **Power (P)** = τω = 15.4 N·m × 27.4 rad/s = 422.0 W
An internal energy increase of 12.8 kJ causes the temperature of the paint to increase by 1.00 K.
**Problem Statement**
If there were no heat flow between the paint and the surroundings, what would be the temperature change of the paint as it is stirred for 5.00 minutes?
\[\_\_\_\_\_ \text{ K}\]
![### Required Information
A contractor uses a paddle stirrer to mix a can of paint. The paddle turns at 27.4 rad/s and exerts a torque of 15.4 N⋅m on the paint, doing work on the paint at a rate of:
\[ \text{Power} = \tau \omega = 15.4 \, \text{N⋅m} \times 27.4 \, \text{rad/s} = 422.0 \, \text{W} \]
An internal energy increase of 12.8 kJ causes the temperature of the paint to increase by 1.00 K.
---
If the actual temperature change was 6.30 K, how much heat flowed from the paint to the surroundings as it is stirred for 5.00 min? Enter the value of \( Q \) in kJ, where positive indicates heat flows into the paint and negative indicates heat flows out of the paint.
\[ \Box \, \text{kJ} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F528734fa-2f56-42f1-ac26-0d1ff4e0efca%2Fc24a0510-b7eb-44e1-9e13-a91e90637bf4%2Ftubtdyf_processed.png&w=3840&q=75)
Transcribed Image Text:### Required Information
A contractor uses a paddle stirrer to mix a can of paint. The paddle turns at 27.4 rad/s and exerts a torque of 15.4 N⋅m on the paint, doing work on the paint at a rate of:
\[ \text{Power} = \tau \omega = 15.4 \, \text{N⋅m} \times 27.4 \, \text{rad/s} = 422.0 \, \text{W} \]
An internal energy increase of 12.8 kJ causes the temperature of the paint to increase by 1.00 K.
---
If the actual temperature change was 6.30 K, how much heat flowed from the paint to the surroundings as it is stirred for 5.00 min? Enter the value of \( Q \) in kJ, where positive indicates heat flows into the paint and negative indicates heat flows out of the paint.
\[ \Box \, \text{kJ} \]
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