The problem states that for every 2 psi drop in pressure, the temperature rises by 3 degrees. This indicates…

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The problem states that for every 2 psi drop in pressure, the temperature rises by 3 degrees. This indicates a linear relationship between temperature and pressure, T = mP + c.

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Here are the solutions to your questions: Question 3 1. Derive the formula which shows the interrelationship between pressure and temperature. Let P be the pressure in psi and T be the temperature in degrees. The problem states that for every 2 psi drop in pressure, the temperature rises by 3 degrees. This indicates a linear relationship between temperature and pressure, T = mP + c. Step 1: Determine the slope (m). The change in pressure is Δ P = −2 psi (pressure drops). The change in temperature is Δ T = +3 degrees (temperature rises). The slope m is given by: m = (Δ T)/(Δ P) = (3)/(−2) = −3/2 Step 2: Use the given point to find the y-intercept (c). We are given that when the pressure is P = 2 psi, the temperature is T = −12 degrees. Substitute these values and the slope into the linear equation T = mP + c: −12 = (−3/2)(2) + c; −12 = −3 + c Step 3: Solve for c. c = −12 + 3; c = −9 Step 4: Write the final formula. Substitute the slope m = −3/2 and the y-intercept c = −9 into T = mP + c: T = −3/2P − 9 The formula showing the interrelationship between pressure and temperature is: T = −3/2P − 9 2. Draw the graph of the above function, show the intersection points on the graph with the axes precisely. The function is T = −3/2P − 9. To draw the graph, we find the intercepts with the axes. Step 1: Find the T-intercept (where P=0). Substitute P=0 into the equation: T = −3/2(0) − 9; T = −9 The T-intercept is (0, −9). Step 2: Find the P-intercept (where T=0). Substitute T=0 into the equation: 0 = −3/2P − 9 Add 9 to both sides: 9 = −3/2P Multiply by −2/3 to solve for P: P = 9 × (−2/3); P = −3 × 2; P = −6 The P-intercept is (−6, 0). Step 3: Draw the graph. Plot the two intercepts (0, −9) and (−6, 0) and draw a straight line through them. The horizontal axis represents Pressure (P in psi) and the vertical axis represents Temperature (T in degrees). ` ^ T (degrees)

The problem states that for every 2 psi drop in pressure, the temperature rises by 3 degrees. This indicates a linear relationship between temperature and pressure, T = mP + c.

Question 3

1. Derive the formula which shows the interrelationship between pressure and temperature.

2. Draw the graph of the above function, show the intersection points on the graph with the axes precisely.

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