Consider the following hypotheses: 12:V ) >(x)) Use rules of inference to prove that the following conclusion follows from th
ese hypotheses: Clearly label the inference rules used at every step of your proof 2. Consider the following hypotheses: H1 Vr (C()--A(x)) H2 : Vr (A() Vy B(y)) Use rules of inference to prove that the following conclusion follows C: 3r (B(x) AC()) H3: Br A(a) from these hypotheses: Clearly label the inference rules used at every step of your proof. 3. Consider the following predicate quantified formula: r y (P(x, y)P(, y)) Prove the unsatisfiability of this formula using rules of inference.
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Answer:
W = 3.12 J
Explanation:
Given the volume is 1.50*10^-3 m^3 and the coefficient of volume for aluminum is β = 69*10^-6 (°C)^-1. The temperature rises from 22°C to 320°C. The difference in temperature is 320 - 22 = 298°C, so ΔT = 298°C. To reiterate our known values we have:
β = 69*10^-6 (°C)^-1 V = 1.50*10^-3 m^3 ΔT = 298°C
So we can plug into the thermal expansion equation to find ΔV which is how much the volume expanded (I'll use d instead of Δ because of format):
So ΔV = 3.0843*10^-5 m^3
Now we have ΔV, next we have to solve for the work done by thermal expansion. The air pressure is 1.01 * 10^5 Pa
To get work, multiply the air pressure and the volume change.
W = 3.12 J
Hope this helps!